dmitriihook/qwq-32b-planning-mystery-16-24k-greedy

distilabel pipeline run --config "https://huggingface.co/datasets/dmitriihook/qwq-32b-planning-mystery-16-24k-greedy/raw/main/pipeline.yaml"

distilabel pipeline info --config "https://huggingface.co/datasets/dmitriihook/qwq-32b-planning-mystery-16-24k-greedy/raw/main/pipeline.yaml"

{
    "Number of blocks": 4,
    "distilabel_metadata": {
        "raw_input_text_generation_0": [
            {
                "content": "I am playing with a set of objects. Here are the actions I can do\n\n   Illuminate object\n   Divest object from another object\n   Silence object\n   Distill object from another object\n\nI have the following restrictions on my actions:\n    To perform Illuminate action, the following facts need to be true: Essence object, Aura object, Nexus.\n    Once Illuminate action is performed the following facts will be true: Pulse object.\n    Once Illuminate action is performed the following facts will be false: Essence object, Aura object, Nexus.\n    To perform Silence action, the following facts need to be true: Pulse object.\n    Once Silence action is performed the following facts will be true: Essence object, Aura object, Nexus.    \n    Once Silence action is performed the following facts will be false: Pulse object.\n    To perform Distill action, the following needs to be true: Essence other object, Pulse object.\n    Once Distill action is performed the following will be true: Nexus, Essence object, Object Harmonizes other object.\n    Once Distill action is performed the following will be false: Essence other object, Pulse object.\n    To perform Divest action, the following needs to be true: Object Harmonizes other object, Essence object, Nexus.\n    Once Divest action is performed the following will be true: Pulse object, Essence other object.\n    Once Divest action is performed the following will be false:, Object Harmonizes other object, Essence object, Nexus.\n\nHere is an example problem:\n\n[STATEMENT]\nAs initial conditions I have that, essence Block B, essence Block C, nexus, Block C harmonizes Block A, aura Block A, aura Block B.\nMy goal is to have that Block A harmonizes Block C and Block B harmonizes Block A.\n\nMy plan is as follows:\n\n[PLAN]\ndivest Block C from Block A\nsilence Block C\nilluminate Block A\ndistill Block A from Block C\nilluminate Block B\ndistill Block B from Block A\n[PLAN END]\n\nHere is another example:\n\n[STATEMENT]\nAs initial conditions I have that, essence Block B, nexus, Block A harmonizes Block D, Block B harmonizes Block C, Block C harmonizes Block A, aura Block D.\nMy goal is to have that Block C harmonizes Block D, Block A harmonizes Block C and Block B harmonizes Block A.\n\nMy plan is as follows:\n\n[PLAN]\ndivest Block B from Block C\nsilence Block B\ndivest Block C from Block A\nsilence Block C\ndivest Block A from Block D\nsilence Block A\nilluminate Block C\ndistill Block C from Block D\nilluminate Block A\ndistill Block A from Block C\nilluminate Block B\ndistill Block B from Block A\n[PLAN END]\nHere is the problem to solve:\n\n[STATEMENT]\nAs initial conditions I have that: aura Block A, aura Block B, aura Block D, essence Block A, essence Block C, essence Block D, Block C harmonizes Block B and nexus.\nMy goal is for the following to be true: Block A harmonizes Block D, Block B harmonizes Block C and Block D harmonizes Block B.\n\nMy plan is as follows:",
                "role": "user"
            }
        ],
        "raw_output_text_generation_0": "Okay, let\u0027s see. I need to solve this problem using the given actions and their conditions. The initial conditions are: aura on A, B, D; essence on A, C, D; C harmonizes B; and there\u0027s a nexus. The goal is to have A harmonizes D, B harmonizes C, and D harmonizes B. Hmm, so the goal is a bit of a cycle here between B, C, and D, and also A with D.\n\nFirst, I should recall the actions and their prerequisites. Let me list them again to make sure I have them right.\n\nThe actions are:\n\n1. **Illuminate object**: Requires Essence, Aura, and Nexus. After doing this, Pulse is true, and Essence, Aura, Nexus are false.\n2. **Divest object from another object**: Needs Object Harmonizes other object, Essence of the first object, and Nexus. After, Pulse of the first object and Essence of the other become true, while Object Harmonizes, Essence, and Nexus are false.\n3. **Silence object**: Requires Pulse. After, Essence, Aura, Nexus become true again, and Pulse is false.\n4. **Distill object from another object**: Needs Essence of the other object and Pulse of the first. After, Nexus, Essence of the first, and Object Harmonizes other become true. The other\u0027s Essence and the first\u0027s Pulse are false.\n\nThe goal is to get A harmonizes D, B harmonizes C, and D harmonizes B. Let me note that the current harmonizes are C harmonizes B. So we need to create two more harmonizes: A-D and D-B, and also ensure B-C is there. Wait, the goal says B harmonizes C and D harmonizes B. So B-C and D-B. Since C already harmonizes B, maybe that can be part of the process?\n\nLet me start by looking at the initial state:\n\n- Essence: A, C, D\n- Aura: A, B, D\n- Nexus: present\n- Harmonizes: C harmonizes B\n\nFirst, I need to figure out a sequence of actions that can lead to the desired harmonizes. Let\u0027s think step by step.\n\nThe goal requires A harmonizes D. To get that, maybe we can use the Distill action. Because Distill requires Essence of the other object and Pulse of the first. Let\u0027s see: To get A harmonizes D, perhaps we need to distill A from D? Wait, the Distill action is \"Distill object from another object\", so the first object is the one being distilled from the second. The result is that the first object harmonizes the second? Wait, the Distill action\u0027s result says \"Object Harmonizes other object\" becomes true. Wait, the Distill action\u0027s description says:\n\nOnce Distill is performed, the following will be true: Nexus, Essence object, Object Harmonizes other object. So the object (the first parameter) harmonizes the other object (the second parameter). So to get A harmonizes D, we need to do Distill A from D? Wait, no. Wait, the parameters are \"Distill object from another object\". So the first object is the one being distilled from the second. Wait, maybe the first object is the one that ends up harmonizing the second. Let me check the Distill action again:\n\n\"Distill object from another object\" requires Essence of the other object and Pulse of the first. After, the following are true: Nexus, Essence of the object (the first?), and Object Harmonizes other object (so the first object harmonizes the second). Wait, the wording is a bit ambiguous. Let me parse the exact description:\n\n\"Once Distill action is performed the following will be true: Nexus, Essence object, Object Harmonizes other object.\"\n\nAh, so \"Essence object\" (the first object) and \"Object Harmonizes other object\" (the first object harmonizes the second). So yes, Distill object (first) from another object (second) will result in the first object harmonizing the second. So to get A harmonizes D, we need to do Distill A from D. But for that, we need Essence of the other object (D) and Pulse of the first (A). \n\nSo to do Distill A from D, we need:\n\n- Essence of D (which we have initially)\n- Pulse of A (so we need to get Pulse on A first)\n\nTo get Pulse on A, we can do Illuminate on A. But Illuminate requires Essence, Aura, and Nexus. For A, we have Essence and Aura, and Nexus is present. So yes, we can Illuminate A. But doing that would set Pulse A to true, and remove Essence, Aura, and Nexus. Wait, but Nexus is a global fact? Or is it per object? The problem says \"Nexus\" as a fact, so it\u0027s a global fact. So if we Illuminate A, then after that, Nexus would be false. That might be a problem because some actions require Nexus. Hmm, so maybe we need to plan carefully.\n\nAlternatively, perhaps we can first use other actions to set up the required conditions without losing Nexus too early.\n\nAlternatively, maybe we can use Divest first. Let\u0027s see.\n\nLooking at the Divest action: To perform Divest object from another object, the prerequisites are:\n\n- Object Harmonizes other object (so the first object harmonizes the second)\n- Essence of the first object\n- Nexus.\n\nAfter Divest, the following become true: Pulse of the first object, Essence of the other object. And the following become false: Object Harmonizes, Essence of the first, Nexus.\n\nSo Divest can be used to get Pulse on the first object, but it requires that the first object already harmonizes the second. \n\nIn the initial state, C harmonizes B. So if we do Divest C from B, that would require:\n\n- C harmonizes B (which is true)\n- Essence of C (which is true)\n- Nexus (true)\n\nSo Divesting C from B would result in:\n\n- Pulse C becomes true\n- Essence B becomes true (since the other object is B)\n- The following become false: C harmonizes B, Essence C, Nexus.\n\nWait, but after Divest, the Object Harmonizes (C harmonizes B) is false, Essence C is false, and Nexus is false. That might be a problem because Nexus is needed for some actions. But maybe that\u0027s a path to take.\n\nAlternatively, perhaps we can first use Divest on C from B to get Pulse on C, then use that Pulse to do something else.\n\nAlternatively, let\u0027s think of the goal again. The goal requires three harmonizes: A-D, B-C, D-B. Wait, D harmonizes B? Or is it B harmonizes D? Wait the problem says \"Block B harmonizes Block C and Block D harmonizes Block B.\" So B-C and D-B. So D must harmonize B, and B must harmonize C. Also, A must harmonize D.\n\nHmm. Let\u0027s see. Let\u0027s try to outline a possible path.\n\nFirst, maybe start with Divesting C from B (since C already harmonizes B). Let\u0027s try that step.\n\nStep 1: Divest C from B.\n\nPrerequisites: C harmonizes B (yes), Essence C (yes), Nexus (yes). So possible.\n\nAfter Divest C from B:\n\n- Pulse C is true\n- Essence B is true (since the other object is B)\n- The following become false: C harmonizes B, Essence C, Nexus.\n\nSo now, the state after this action:\n\n- Essence: B (since Essence C is now false, and Essence A and D were already there, but wait, original Essence was A, C, D. After Divest, Essence C is removed, so Essence remains A, D, and B (from the Divest\u0027s result). Wait, the Divest action\u0027s result says \"Essence other object\" becomes true. The other object here is B, so Essence B is set to true. So yes, Essence B is now present.\n\nAura: A, B, D (unchanged, since Divest doesn\u0027t affect Aura)\n\nNexus: becomes false (because Divest\u0027s effect includes making Nexus false)\n\nPulse C is now true.\n\nHarmonizes: C no longer harmonizes B (since that fact is removed), so the only harmonize is whatever else, but initially only C-B was there, so now none.\n\nHmm, but now Nexus is gone, which might be a problem because some actions require Nexus. For example, Illuminate requires Nexus. So maybe this is a bad path. Let\u0027s see if we can proceed.\n\nAlternatively, maybe we can Silence an object to get Nexus back. Let\u0027s see.\n\nAfter Divest C from B, we have Pulse C. So we can Silence C. Let\u0027s try that.\n\nStep 2: Silence C.\n\nPrerequisites: Pulse C (yes). After Silence:\n\n- Essence, Aura, Nexus become true again (since Silence\u0027s effect is to set those to true)\n- Pulse C becomes false.\n\nSo after Silence C:\n\n- Essence: A, D, B (since Essence was already there except C, but Silence doesn\u0027t affect Essence except for the object being silenced? Wait, the Silence action\u0027s effect says \"Once Silence is performed the following will be true: Essence object, Aura object, Nexus.\" So for the object being silenced (C), its Essence, Aura, and Nexus are set to true? Wait, no. Wait, the Silence action is on an object, so the description says:\n\n\"Once Silence action is performed the following will be true: Essence object, Aura object, Nexus. Once Silence action is performed the following will be false: Pulse object.\"\n\nWait, the Silence action on object X will set Essence X, Aura X, and Nexus to true? Or is it that for the object, those are set? The wording is a bit ambiguous. Let me check again.\n\nThe Silence action\u0027s description says:\n\n\"To perform Silence action, the following needs to be true: Pulse object.\n\nOnce Silence action is performed the following will be true: Essence object, Aura object, Nexus.\n\nOnce Silence action is performed the following will be false: Pulse object.\"\n\nAh, so Silence on object X requires that X has Pulse. After Silence, the following facts become true: Essence X, Aura X, and Nexus (the global Nexus). And Pulse X becomes false.\n\nSo in our case, after Divesting C from B and then Silencing C:\n\n- Essence C is now true (because Silence sets Essence C to true)\n- Aura C is now true (since Silence sets Aura C to true)\n- Nexus is now true again (since Silence sets Nexus to true)\n- Pulse C is false.\n\nSo the state after Silence C:\n\n- Essence: A, C, D, B (since Divest had set Essence B to true, and Silence adds back Essence C)\n- Aura: A, B, D, C (since Silence adds Aura C)\n- Nexus: true\n- Pulse C: false\n- Harmonizes: none (since Divest removed C harmonizes B, and nothing else was there)\n\nHmm, that\u0027s better. So now we can proceed with other actions.\n\nNow, perhaps we can try to get A harmonizes D. To do that, we need to do Distill A from D. Let\u0027s see what\u0027s needed for that.\n\nDistill A from D requires:\n\n- Essence of the other object (D) must be true (which it is)\n- Pulse of the first object (A) must be true.\n\nSo we need to get Pulse A. To get Pulse A, we can Illuminate A. Let\u0027s try that.\n\nStep 3: Illuminate A.\n\nPrerequisites: Essence A (yes), Aura A (yes), Nexus (yes). So possible.\n\nAfter Illuminate A:\n\n- Pulse A becomes true\n- Essence A, Aura A, and Nexus become false.\n\nSo now:\n\n- Essence: C, D, B (since A\u0027s Essence is now false)\n- Aura: B, D, C (A\u0027s Aura is now false)\n- Nexus: false (because Illuminate set it to false)\n- Pulse A: true\n- Harmonizes: still none.\n\nHmm, but now Nexus is false again. But we need to do Distill A from D, which requires Pulse A (which we have) and Essence D (which is true). So let\u0027s proceed.\n\nStep 4: Distill A from D.\n\nPrerequisites: Essence D (yes) and Pulse A (yes). So yes.\n\nAfter Distill A from D:\n\n- The following become true: Nexus, Essence A (the first object), and A harmonizes D (since the first object is A, harmonizes the second D).\n\n- The following become false: Essence D (since it\u0027s the other object) and Pulse A (the first object\u0027s pulse).\n\nSo after Distill:\n\n- Essence: A (from the result), C, B (since D\u0027s Essence is now false)\n- Aura: B, D (since D\u0027s Aura was still present? Wait, Aura isn\u0027t affected by Distill. Let me check the Distill effects again.\n\nWait, the Distill action\u0027s effects are:\n\n\"Once Distill action is performed the following will be true: Nexus, Essence object, Object Harmonizes other object.\n\nOnce Distill action is performed the following will be false: Essence other object, Pulse object.\"\n\nSo for Distill A from D:\n\n- True: Nexus (so global Nexus is true again), Essence A (so A\u0027s Essence is true again), and A harmonizes D.\n\n- False: Essence D (so D\u0027s Essence is now false), Pulse A (so Pulse A is false).\n\nAura is not mentioned, so Aura remains as before. So Aura D was still present (since we only set Essence D to false, not Aura). Wait, the initial Aura D was present, and in the steps before, when we did Divest and Silence, Aura D was still there. So after Distill, Aura D is still present unless changed. So Aura remains A (no, A\u0027s Aura was turned off by Illuminate, but after Distill, does it change? No, only the facts listed in the action\u0027s effects are changed. So Aura A is still false (from Illuminate), but others are as before except D\u0027s Essence.\n\nSo after Distill A from D:\n\n- Essence: A, C, B (since D\u0027s Essence is now false)\n- Aura: B, D, C (since A\u0027s Aura is still false)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse A: false\n- Harmonizes: A harmonizes D (new), and any others? No, since previous harmonizes were erased.\n\nNow, the goal requires A harmonizes D, which is done. Now we need B harmonizes C and D harmonizes B. Let\u0027s see.\n\nFirst, let\u0027s note that D\u0027s Essence is now false. So we can\u0027t use D in some actions unless we get its Essence back. Also, D\u0027s Aura is still present (since Aura wasn\u0027t touched here).\n\nLooking at the current state:\n\n- Essence: A, B, C\n- Aura: B, D, C\n- Nexus: true\n- Pulse A: false\n- Harmonizes: A-D\n\nWe need to get B harmonizes C and D harmonizes B. Let\u0027s see how to get those.\n\nTo get B harmonizes C, perhaps we can do a Distill of B from C. Let\u0027s see:\n\nDistill B from C requires:\n\n- Essence of the other object (C) must be true (yes)\n- Pulse of B must be true.\n\nTo get Pulse B, we can do Illuminate B. Let\u0027s see if that\u0027s possible.\n\nTo Illuminate B, we need Essence B (yes), Aura B (yes), and Nexus (yes). So yes.\n\nStep 5: Illuminate B.\n\nPrerequisites: Essence B (yes), Aura B (yes), Nexus (yes). So possible.\n\nAfter Illuminate B:\n\n- Pulse B becomes true\n- Essence B, Aura B, Nexus become false.\n\nSo now:\n\n- Essence: A, C (since B\u0027s Essence is now false)\n- Aura: D, C (B\u0027s Aura is now false)\n- Nexus: false\n- Pulse B: true\n- Harmonizes: A-D\n\nNow, with Pulse B, we can do Distill B from C.\n\nStep 6: Distill B from C.\n\nPrerequisites: Essence C (yes) and Pulse B (yes). So yes.\n\nAfter Distill B from C:\n\n- The following become true: Nexus, Essence B (the first object), and B harmonizes C (the second object).\n\n- The following become false: Essence C (since it\u0027s the other object), Pulse B (the first object\u0027s pulse).\n\nSo after Distill:\n\n- Essence: A, B (since C\u0027s Essence is now false)\n- Aura: D, C (Aura C is still present unless changed, but Distill doesn\u0027t affect Aura)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse B: false\n- Harmonizes: A-D, B-C.\n\nNow, we have B harmonizes C, which is part of the goal. Now we need D harmonizes B. \n\nTo get D harmonizes B, we need to have D harmonize B. Let\u0027s see how to do that. \n\nD\u0027s current state: Essence is false (from earlier steps), Aura is still present (since we haven\u0027t touched it). To get D harmonizes B, perhaps we can do a Distill of D from B? Let\u0027s see:\n\nDistill D from B requires:\n\n- Essence of the other object (B) must be true (yes, since Essence B is true now)\n- Pulse of D must be true.\n\nTo get Pulse D, we need to Illuminate D. Let\u0027s see if that\u0027s possible.\n\nTo Illuminate D, we need Essence D (currently false), Aura D (yes), and Nexus (yes). Since Essence D is false, we can\u0027t do that. So we need to get Essence D back.\n\nHow can we get Essence D back? Let\u0027s think. \n\nLooking at the actions, perhaps using Divest or Silence. \n\nAlternatively, maybe we can use Divest on another object. Let\u0027s see.\n\nAlternatively, perhaps we can do a Divest on A from D, but let\u0027s see.\n\nWait, currently, A has Essence (yes), Aura is false (from Illuminate A earlier). To do Divest on A from D, we need:\n\n- A harmonizes D (which is true)\n- Essence A (yes)\n- Nexus (yes).\n\nSo Divest A from D would be possible. Let\u0027s try that.\n\nStep 7: Divest A from D.\n\nPrerequisites: A harmonizes D (yes), Essence A (yes), Nexus (yes). So yes.\n\nAfter Divest A from D:\n\n- Pulse A becomes true\n- Essence D becomes true (since the other object is D)\n- The following become false: A harmonizes D, Essence A, Nexus.\n\nWait, the Divest action\u0027s effects:\n\n\"Once Divest action is performed the following will be true: Pulse object (A), Essence other object (D).\n\nOnce Divest action is performed the following will be false: Object Harmonizes other object (A harmonizes D), Essence object (A), Nexus.\"\n\nSo after Divest A from D:\n\n- Pulse A is true\n- Essence D is true\n- A no longer harmonizes D\n- Essence A is false\n- Nexus is false.\n\nHmm, but we wanted to keep A harmonizes D. That\u0027s a problem. Because the goal requires A harmonizes D. So this might not be the right path. Let\u0027s see if there\u0027s another way.\n\nAlternatively, perhaps we can get D\u0027s Essence back through another method. Let\u0027s think.\n\nAlternatively, after step 6, we have:\n\n- Essence: A (no, wait, after step 6, after Distill B from C, Essence B is set to true (from the Distill\u0027s effect). Wait, let me recheck step 6\u0027s effects.\n\nWait, in step 6, Distill B from C:\n\nThe Distill action\u0027s effect says \"Essence object\" (the first object, which is B) becomes true. So yes, Essence B is true. But what about Essence A? In step 5, when we did Illuminate B, we turned off Essence B, but then in step 6\u0027s Distill, we turned it back on. Wait, let me retrace:\n\nAfter step 5 (Illuminate B):\n\n- Essence B was turned off.\n\nThen step 6 (Distill B from C):\n\n- The Distill action\u0027s effect sets Essence B to true again. So yes, after step 6, Essence B is true again.\n\nSo in step 6\u0027s aftermath:\n\n- Essence: A (from step 4\u0027s Distill A from D, which set Essence A to true again?), wait let me retrace step 4\u0027s Distill A from D.\n\nStep 4: Distill A from D. The effect was \"Essence object (A) becomes true\". So yes, after step 4, Essence A is true. Then step 5 (Illuminate B) only affects B\u0027s Essence, so A\u0027s Essence remains true until step 7?\n\nWait, step 7 was Divest A from D, which would set Essence A to false. But if we don\u0027t do that, then in step 6\u0027s aftermath:\n\n- Essence A is still true (from step 4\u0027s Distill)\n- Essence B is true (from step 6\u0027s Distill)\n- Essence C is false (from step 6\u0027s Distill, since the other object was C, so Essence C is now false)\n- Essence D is false (from step 4\u0027s Distill, which set Essence D to false)\n\nWait, in step 4\u0027s Distill A from D, the other object is D, so Essence D is set to false. So D\u0027s Essence is off.\n\nSo to get D\u0027s Essence back, perhaps we can do a Divest on another object that involves D. Let\u0027s see.\n\nAlternatively, maybe we can do a Silence on D to get its Essence back. Wait, Silence requires Pulse D. To get Pulse D, we need to Illuminate D, but that requires Essence D (which is off). So that\u0027s a problem.\n\nAlternatively, perhaps we can do a Divest on D from another object. Let\u0027s see.\n\nWait, to do Divest D from something, we need that D harmonizes that object, and Essence D, and Nexus. But D\u0027s Essence is off, so that\u0027s not possible.\n\nHmm, tricky. Let\u0027s think of another approach.\n\nWe need D harmonizes B. To get that, perhaps we can do Distill D from B. For that, we need:\n\n- Essence B (which is true)\n- Pulse D (so need to get Pulse D)\n\nTo get Pulse D, we can do Illuminate D, but that requires Essence D (which is off). So unless we can get Essence D back, we can\u0027t do that.\n\nAlternatively, maybe we can get Essence D back via another action. Let\u0027s see.\n\nLooking back, after step 6, the state is:\n\n- Essence: A, B (since Essence C is false, D is false)\n- Aura: D, C (since B\u0027s Aura was turned off in step 5, but D\u0027s Aura is still there)\n- Nexus: true (from step 6\u0027s Distill)\n- Pulse B: false (from step 6\u0027s Distill)\n- Harmonizes: A-D (no, wait, after step 6, when we did Distill B from C, the A-D harmonize was still there? Wait, no. Wait, in step 6\u0027s Distill B from C, the only harmonize added is B-C. The A-D harmonize was from step 4\u0027s Distill, but does it stay?\n\nWait, the Distill B from C doesn\u0027t remove any harmonizes except those explicitly mentioned. The Divest actions remove harmonizes, but Distill only adds a new one. So after step 4\u0027s Distill A from D, A harmonizes D is true. Then step 6\u0027s Distill B from C adds B harmonizes C. So the harmonizes are A-D and B-C. So that\u0027s correct.\n\nNow, to get D harmonizes B, perhaps we can do a Divest on B from D? Wait, but D\u0027s Essence is off. Alternatively, maybe we can do a Divest on D from B, but that requires D harmonizes B, which we don\u0027t have yet. Hmm.\n\nAlternatively, maybe we can do a Divest on A from D again, but that would remove A-D harmonize, which we need. Not good.\n\nAlternatively, let\u0027s think of another path. Let\u0027s see if we can get D\u0027s Essence back through a Divest action involving another object.\n\nWait, perhaps we can do a Divest on C from B. Wait, but C\u0027s Essence is off (from step 6\u0027s Distill B from C, which set Essence C to false). So that\u0027s not possible.\n\nAlternatively, maybe we can do a Silence on D to get its Essence back. Wait, Silence requires Pulse D. To get Pulse D, we need to Illuminate D, but that requires Essence D (which is off). So that\u0027s a loop.\n\nHmm, maybe we need to backtrack and try a different approach.\n\nLet me think again. The problem requires D harmonizes B. To get that, perhaps we can do Distill D from B. To do that, we need:\n\n- Essence B (which is true)\n- Pulse D (so need to get Pulse D)\n\nTo get Pulse D, we can do Illuminate D, but that requires Essence D (which is off). So unless we can get Essence D back, we can\u0027t do that.\n\nAlternatively, maybe we can get Essence D back via a Divest action. Let\u0027s see.\n\nSuppose we do a Divest on A from D (even though it removes A-D harmonize). Let\u0027s see what happens.\n\nStep 7: Divest A from D (as before):\n\nPrerequisites: A harmonizes D (yes), Essence A (yes), Nexus (yes).\n\nAfter Divest:\n\n- Pulse A becomes true\n- Essence D becomes true (since other object is D)\n- A no longer harmonizes D\n- Essence A becomes false\n- Nexus becomes false.\n\nNow, after this, we have:\n\n- Essence: B (since A\u0027s is now false), D (now true)\n- Aura: D, C (since A\u0027s Aura was off, B\u0027s was off)\n- Nexus: false\n- Pulse A: true\n- Harmonizes: B-C (since A-D was removed)\n\nBut now, we lost A-D, which is part of the goal. So that\u0027s bad. But maybe we can fix it later.\n\nNow, with Essence D back, we can try to get D\u0027s Pulse.\n\nStep 8: Illuminate D.\n\nPrerequisites: Essence D (yes), Aura D (yes), Nexus (no, it\u0027s false). So can\u0027t do that.\n\nHmm, Nexus is false here. So that\u0027s a problem.\n\nAlternatively, maybe Silence an object to get Nexus back. Let\u0027s see.\n\nWe can Silence A (since it has Pulse A from step 7). Let\u0027s try that.\n\nStep 8: Silence A.\n\nPrerequisites: Pulse A (yes). After Silence:\n\n- Essence A, Aura A, Nexus become true.\n- Pulse A becomes false.\n\nSo after Silence A:\n\n- Essence: A (now true again), B, D\n- Aura: A (now true), B (still false?), D (yes), C (yes)\nWait, Silence A sets Essence A, Aura A, and Nexus to true. So Aura A is now true again.\n\n- Nexus is now true again.\n\nSo now, after step 8:\n\n- Essence: A, B, D\n- Aura: A, B (since Silence A restored Aura B?), no, wait, the Silence action on A only affects A\u0027s Essence, Aura, and the global Nexus. So Aura B was turned off in step 5 (Illuminate B), and hasn\u0027t been turned back on. So Aura B is still false. So Aura now is A, B (no, wait, Silence A only affects A\u0027s Aura. So Aura B remains false. So Aura is A, D, C.\n\nWait, let me clarify:\n\nAfter step 7 (Divest A from D):\n\nAura was D and C (since B\u0027s was off). Then step 8 (Silence A):\n\n- Silence A sets Essence A, Aura A, and Nexus to true. So Aura A is now true, but Aura B remains as it was (still false from step 5). So Aura now includes A, D, C.\n\nSo after step 8:\n\n- Essence: A (true again), B, D\n- Aura: A, D, C\n- Nexus: true\n- Pulse A: false (from Silence)\n- Harmonizes: B-C (since A-D was removed in step7)\n\nNow, with Essence D and Nexus, we can try to Illuminate D to get Pulse D.\n\nStep 9: Illuminate D.\n\nPrerequisites: Essence D (yes), Aura D (yes), Nexus (yes). So yes.\n\nAfter Illuminate D:\n\n- Pulse D becomes true\n- Essence D, Aura D, Nexus become false.\n\nSo now:\n\n- Essence: A, B (since D\u0027s Essence is now false)\n- Aura: A, C (since D\u0027s Aura is now false)\n- Nexus: false\n- Pulse D: true\n- Harmonizes: B-C\n\nNow, with Pulse D, we can do Distill D from B to get D harmonizes B.\n\nStep 10: Distill D from B.\n\nPrerequisites: Essence B (yes) and Pulse D (yes). So yes.\n\nAfter Distill D from B:\n\n- The following become true: Nexus, Essence D (the first object is D?), wait no. Wait, Distill D from B means the first object is D, the second is B.\n\nWait, Distill D from B requires:\n\n- Essence of the other object (B) must be true (yes)\n- Pulse of D (yes)\n\nAfter Distill D from B:\n\n- True: Nexus, Essence D (the first object, D), and D harmonizes B (the second object, B).\n\n- False: Essence B (since it\u0027s the other object), Pulse D (the first object\u0027s pulse).\n\nSo after this:\n\n- Essence: A, D (since B\u0027s Essence is now false)\n- Aura: A, C (since D\u0027s Aura was turned off in step9, and B\u0027s was already off)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse D: false\n- Harmonizes: B-C, D-B.\n\nNow, we have D harmonizes B (good), and B-C (good). But we lost A\u0027s harmonize with D (since we had to remove it earlier). So we need to get A harmonizes D back.\n\nHmm, so now the harmonizes are B-C and D-B, but A-D is gone. So we need to fix that.\n\nTo get A harmonizes D again, we can do Distill A from D again. Let\u0027s see.\n\nFirst, we need to get Pulse A. Let\u0027s see:\n\nCurrent state after step10:\n\n- Essence: A, D\n- Aura: A, C\n- Nexus: true\n- Pulse D: false\n- Pulse A: ?\n\nPulse A was turned off in step8 (Silence A), and hasn\u0027t been turned back on. So Pulse A is false.\n\nTo get Pulse A, we can Illuminate A again.\n\nStep 11: Illuminate A.\n\nPrerequisites: Essence A (yes), Aura A (yes), Nexus (yes). So yes.\n\nAfter Illuminate A:\n\n- Pulse A becomes true\n- Essence A, Aura A, Nexus become false.\n\nSo now:\n\n- Essence: D (since A\u0027s is now false)\n- Aura: C (since A\u0027s and D\u0027s are off)\n- Nexus: false\n- Pulse A: true\n- Harmonizes: B-C, D-B.\n\nNow, with Pulse A and Essence D (since D\u0027s Essence is still true?), wait, after step10\u0027s Distill D from B, Essence D was set to true (from the Distill\u0027s effect). So yes, Essence D is true.\n\nSo to do Distill A from D again:\n\nStep 12: Distill A from D.\n\nPrerequisites: Essence D (yes) and Pulse A (yes). So yes.\n\nAfter Distill A from D:\n\n- True: Nexus, Essence A (the first object), A harmonizes D (the second object D)\n- False: Essence D (since it\u0027s the other object), Pulse A (the first object\u0027s pulse)\n\nSo after this:\n\n- Essence: A (from Distill\u0027s effect), D is now false (since it\u0027s the other object)\n- Aura: C (since A\u0027s Aura was turned off in step11, D\u0027s was off)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse A: false\n- Harmonizes: A-D (new), B-C, D-B (wait, does D-B still hold?)\n\nWait, the Distill A from D doesn\u0027t affect existing harmonizes unless they are explicitly removed. The only harmonize added is A-D. The existing B-C and D-B remain unless an action removes them. Since we didn\u0027t do any Divest that would remove them, they should still be there.\n\nSo now, after step12, the harmonizes are A-D, B-C, D-B. Which is exactly the goal!\n\nSo the final state meets all the goals. Let\u0027s check the steps again to make sure there are no errors.\n\nLet me recap the steps:\n\n1. Divest C from B \u2192 gets Pulse C, Essence B, loses C harmonizes B, loses Nexus, Essence C.\n2. Silence C \u2192 restores Essence C, Aura C, Nexus; Pulse C off.\n3. Illuminate A \u2192 gets Pulse A, loses Essence A, Aura A, Nexus.\n4. Distill A from D \u2192 gets A harmonizes D, Nexus, Essence A; loses Essence D, Pulse A.\n5. Illuminate B \u2192 gets Pulse B, loses Essence B, Aura B, Nexus.\n6. Distill B from C \u2192 gets B harmonizes C, Essence B, Nexus; loses Essence C, Pulse B.\n7. Divest A from D \u2192 removes A-D, gets Pulse A, Essence D; loses Essence A, Nexus.\n8. Silence A \u2192 restores Essence A, Aura A, Nexus; Pulse A off.\n9. Illuminate D \u2192 gets Pulse D, loses Essence D, Aura D, Nexus.\n10. Distill D from B \u2192 gets D harmonizes B, Essence D, Nexus; loses Essence B, Pulse D.\n11. Illuminate A \u2192 gets Pulse A, loses Essence A, Aura A, Nexus.\n12. Distill A from D \u2192 gets A harmonizes D, Essence A, Nexus; loses Essence D, Pulse A.\n\nWait, but in step 10, after Distill D from B, Essence B was set to false (since the other object is B, so Essence B becomes false). Then in step 11, when we Illuminate A, we need Essence A (which was restored in step8, but in step7 Divest A from D turned off Essence A, then step8 Silence A turned it back on. So yes, step11 can do Illuminate A.\n\nBut after step10, Essence B is false. So in step10\u0027s aftermath, Essence B is off. Then in step12, after Distill A from D, Essence D is off again. But the final harmonizes are all there.\n\nThis seems to work, but the path is quite long. Let me see if there\u0027s a shorter way.\n\nAlternatively, maybe there\u0027s a different sequence that avoids some steps. Let me think again.\n\nAlternative approach:\n\nStarting over, perhaps after getting A harmonizes D and B harmonizes C, we can find a way to get D harmonizes B without losing A-D.\n\nLet me try another path.\n\nStarting from the initial state:\n\nInitial:\n\n- Essence: A, C, D\n- Aura: A, B, D\n- Nexus: yes\n- Harmonizes: C-B\n\nGoal: A-D, B-C, D-B.\n\nFirst, let\u0027s try to get B-C first via Divest and Distill, then proceed.\n\nStep 1: Divest C from B (as before). Then Silence C, getting back Essence C, etc.\n\nThen, proceed to get A-D via Illuminate A, Distill A from D.\n\nThen, to get D-B, perhaps instead of going through the long path, let\u0027s see:\n\nAfter step 4 (Distill A from D), we have A-D, and Essence D is off. To get D-B, perhaps we can do:\n\nStep 5: Divest A from D (to get Essence D back and Pulse A, but lose A-D). Then Silence A to get back Essence A and Nexus.\n\nThen Illuminate D to get Pulse D, then Distill D from B (but need Essence B).\n\nWait, this is similar to the previous path. It might be necessary to go through those steps.\n\nAlternatively, after step 4 (Distill A from D), we have:\n\n- Essence: A, B, C (since Divest C from B gave Essence B, and Silence C restored Essence C)\nWait, no, let me retrace:\n\nWait, in the first path, after step4 (Distill A from D), the Essence D is off, but Essence B and C are present?\n\nHmm, perhaps there\u0027s a smarter way. Alternatively, maybe the initial plan is the way to go, even if it\u0027s long.\n\nAlternatively, let\u0027s see the example plans given. In the first example, the plan had Divest, Silence, Illuminate, Distill, etc. The second example had multiple Divest and Silence steps. So perhaps the solution requires multiple cycles of Divest, Silence, Illuminate, Distill.\n\nGiven that, the path I outlined earlier works, even if it\u0027s lengthy. Let me check if all steps are valid and the final state meets the goals.\n\nYes, in the final step (step12), the harmonizes are A-D, B-C, D-B, which is exactly the goal. The other facts like Essence and Aura might not matter as long as the harmonizes are there. The problem only specifies the goal as the harmonizes, so that\u0027s okay.\n\nTherefore, the plan would be the sequence of steps I outlined. Let me write them in order as per the required format.\n\u003c/think\u003e\n\n[PLAN]\ndivest Block C from Block B\nsilence Block C\nilluminate Block A\ndistill Block A from Block D\nilluminate Block B\ndistill Block B from Block C\ndivest Block A from Block D\nsilence Block A\nilluminate Block D\ndistill Block D from Block B\nilluminate Block A\ndistill Block A from Block D\n[PLAN END]",
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    "generation": "Okay, let\u0027s see. I need to solve this problem using the given actions and their conditions. The initial conditions are: aura on A, B, D; essence on A, C, D; C harmonizes B; and there\u0027s a nexus. The goal is to have A harmonizes D, B harmonizes C, and D harmonizes B. Hmm, so the goal is a bit of a cycle here between B, C, and D, and also A with D.\n\nFirst, I should recall the actions and their prerequisites. Let me list them again to make sure I have them right.\n\nThe actions are:\n\n1. **Illuminate object**: Requires Essence, Aura, and Nexus. After doing this, Pulse is true, and Essence, Aura, Nexus are false.\n2. **Divest object from another object**: Needs Object Harmonizes other object, Essence of the first object, and Nexus. After, Pulse of the first object and Essence of the other become true, while Object Harmonizes, Essence, and Nexus are false.\n3. **Silence object**: Requires Pulse. After, Essence, Aura, Nexus become true again, and Pulse is false.\n4. **Distill object from another object**: Needs Essence of the other object and Pulse of the first. After, Nexus, Essence of the first, and Object Harmonizes other become true. The other\u0027s Essence and the first\u0027s Pulse are false.\n\nThe goal is to get A harmonizes D, B harmonizes C, and D harmonizes B. Let me note that the current harmonizes are C harmonizes B. So we need to create two more harmonizes: A-D and D-B, and also ensure B-C is there. Wait, the goal says B harmonizes C and D harmonizes B. So B-C and D-B. Since C already harmonizes B, maybe that can be part of the process?\n\nLet me start by looking at the initial state:\n\n- Essence: A, C, D\n- Aura: A, B, D\n- Nexus: present\n- Harmonizes: C harmonizes B\n\nFirst, I need to figure out a sequence of actions that can lead to the desired harmonizes. Let\u0027s think step by step.\n\nThe goal requires A harmonizes D. To get that, maybe we can use the Distill action. Because Distill requires Essence of the other object and Pulse of the first. Let\u0027s see: To get A harmonizes D, perhaps we need to distill A from D? Wait, the Distill action is \"Distill object from another object\", so the first object is the one being distilled from the second. The result is that the first object harmonizes the second? Wait, the Distill action\u0027s result says \"Object Harmonizes other object\" becomes true. Wait, the Distill action\u0027s description says:\n\nOnce Distill is performed, the following will be true: Nexus, Essence object, Object Harmonizes other object. So the object (the first parameter) harmonizes the other object (the second parameter). So to get A harmonizes D, we need to do Distill A from D? Wait, no. Wait, the parameters are \"Distill object from another object\". So the first object is the one being distilled from the second. Wait, maybe the first object is the one that ends up harmonizing the second. Let me check the Distill action again:\n\n\"Distill object from another object\" requires Essence of the other object and Pulse of the first. After, the following are true: Nexus, Essence of the object (the first?), and Object Harmonizes other object (so the first object harmonizes the second). Wait, the wording is a bit ambiguous. Let me parse the exact description:\n\n\"Once Distill action is performed the following will be true: Nexus, Essence object, Object Harmonizes other object.\"\n\nAh, so \"Essence object\" (the first object) and \"Object Harmonizes other object\" (the first object harmonizes the second). So yes, Distill object (first) from another object (second) will result in the first object harmonizing the second. So to get A harmonizes D, we need to do Distill A from D. But for that, we need Essence of the other object (D) and Pulse of the first (A). \n\nSo to do Distill A from D, we need:\n\n- Essence of D (which we have initially)\n- Pulse of A (so we need to get Pulse on A first)\n\nTo get Pulse on A, we can do Illuminate on A. But Illuminate requires Essence, Aura, and Nexus. For A, we have Essence and Aura, and Nexus is present. So yes, we can Illuminate A. But doing that would set Pulse A to true, and remove Essence, Aura, and Nexus. Wait, but Nexus is a global fact? Or is it per object? The problem says \"Nexus\" as a fact, so it\u0027s a global fact. So if we Illuminate A, then after that, Nexus would be false. That might be a problem because some actions require Nexus. Hmm, so maybe we need to plan carefully.\n\nAlternatively, perhaps we can first use other actions to set up the required conditions without losing Nexus too early.\n\nAlternatively, maybe we can use Divest first. Let\u0027s see.\n\nLooking at the Divest action: To perform Divest object from another object, the prerequisites are:\n\n- Object Harmonizes other object (so the first object harmonizes the second)\n- Essence of the first object\n- Nexus.\n\nAfter Divest, the following become true: Pulse of the first object, Essence of the other object. And the following become false: Object Harmonizes, Essence of the first, Nexus.\n\nSo Divest can be used to get Pulse on the first object, but it requires that the first object already harmonizes the second. \n\nIn the initial state, C harmonizes B. So if we do Divest C from B, that would require:\n\n- C harmonizes B (which is true)\n- Essence of C (which is true)\n- Nexus (true)\n\nSo Divesting C from B would result in:\n\n- Pulse C becomes true\n- Essence B becomes true (since the other object is B)\n- The following become false: C harmonizes B, Essence C, Nexus.\n\nWait, but after Divest, the Object Harmonizes (C harmonizes B) is false, Essence C is false, and Nexus is false. That might be a problem because Nexus is needed for some actions. But maybe that\u0027s a path to take.\n\nAlternatively, perhaps we can first use Divest on C from B to get Pulse on C, then use that Pulse to do something else.\n\nAlternatively, let\u0027s think of the goal again. The goal requires three harmonizes: A-D, B-C, D-B. Wait, D harmonizes B? Or is it B harmonizes D? Wait the problem says \"Block B harmonizes Block C and Block D harmonizes Block B.\" So B-C and D-B. So D must harmonize B, and B must harmonize C. Also, A must harmonize D.\n\nHmm. Let\u0027s see. Let\u0027s try to outline a possible path.\n\nFirst, maybe start with Divesting C from B (since C already harmonizes B). Let\u0027s try that step.\n\nStep 1: Divest C from B.\n\nPrerequisites: C harmonizes B (yes), Essence C (yes), Nexus (yes). So possible.\n\nAfter Divest C from B:\n\n- Pulse C is true\n- Essence B is true (since the other object is B)\n- The following become false: C harmonizes B, Essence C, Nexus.\n\nSo now, the state after this action:\n\n- Essence: B (since Essence C is now false, and Essence A and D were already there, but wait, original Essence was A, C, D. After Divest, Essence C is removed, so Essence remains A, D, and B (from the Divest\u0027s result). Wait, the Divest action\u0027s result says \"Essence other object\" becomes true. The other object here is B, so Essence B is set to true. So yes, Essence B is now present.\n\nAura: A, B, D (unchanged, since Divest doesn\u0027t affect Aura)\n\nNexus: becomes false (because Divest\u0027s effect includes making Nexus false)\n\nPulse C is now true.\n\nHarmonizes: C no longer harmonizes B (since that fact is removed), so the only harmonize is whatever else, but initially only C-B was there, so now none.\n\nHmm, but now Nexus is gone, which might be a problem because some actions require Nexus. For example, Illuminate requires Nexus. So maybe this is a bad path. Let\u0027s see if we can proceed.\n\nAlternatively, maybe we can Silence an object to get Nexus back. Let\u0027s see.\n\nAfter Divest C from B, we have Pulse C. So we can Silence C. Let\u0027s try that.\n\nStep 2: Silence C.\n\nPrerequisites: Pulse C (yes). After Silence:\n\n- Essence, Aura, Nexus become true again (since Silence\u0027s effect is to set those to true)\n- Pulse C becomes false.\n\nSo after Silence C:\n\n- Essence: A, D, B (since Essence was already there except C, but Silence doesn\u0027t affect Essence except for the object being silenced? Wait, the Silence action\u0027s effect says \"Once Silence is performed the following will be true: Essence object, Aura object, Nexus.\" So for the object being silenced (C), its Essence, Aura, and Nexus are set to true? Wait, no. Wait, the Silence action is on an object, so the description says:\n\n\"Once Silence action is performed the following will be true: Essence object, Aura object, Nexus. Once Silence action is performed the following will be false: Pulse object.\"\n\nWait, the Silence action on object X will set Essence X, Aura X, and Nexus to true? Or is it that for the object, those are set? The wording is a bit ambiguous. Let me check again.\n\nThe Silence action\u0027s description says:\n\n\"To perform Silence action, the following needs to be true: Pulse object.\n\nOnce Silence action is performed the following will be true: Essence object, Aura object, Nexus.\n\nOnce Silence action is performed the following will be false: Pulse object.\"\n\nAh, so Silence on object X requires that X has Pulse. After Silence, the following facts become true: Essence X, Aura X, and Nexus (the global Nexus). And Pulse X becomes false.\n\nSo in our case, after Divesting C from B and then Silencing C:\n\n- Essence C is now true (because Silence sets Essence C to true)\n- Aura C is now true (since Silence sets Aura C to true)\n- Nexus is now true again (since Silence sets Nexus to true)\n- Pulse C is false.\n\nSo the state after Silence C:\n\n- Essence: A, C, D, B (since Divest had set Essence B to true, and Silence adds back Essence C)\n- Aura: A, B, D, C (since Silence adds Aura C)\n- Nexus: true\n- Pulse C: false\n- Harmonizes: none (since Divest removed C harmonizes B, and nothing else was there)\n\nHmm, that\u0027s better. So now we can proceed with other actions.\n\nNow, perhaps we can try to get A harmonizes D. To do that, we need to do Distill A from D. Let\u0027s see what\u0027s needed for that.\n\nDistill A from D requires:\n\n- Essence of the other object (D) must be true (which it is)\n- Pulse of the first object (A) must be true.\n\nSo we need to get Pulse A. To get Pulse A, we can Illuminate A. Let\u0027s try that.\n\nStep 3: Illuminate A.\n\nPrerequisites: Essence A (yes), Aura A (yes), Nexus (yes). So possible.\n\nAfter Illuminate A:\n\n- Pulse A becomes true\n- Essence A, Aura A, and Nexus become false.\n\nSo now:\n\n- Essence: C, D, B (since A\u0027s Essence is now false)\n- Aura: B, D, C (A\u0027s Aura is now false)\n- Nexus: false (because Illuminate set it to false)\n- Pulse A: true\n- Harmonizes: still none.\n\nHmm, but now Nexus is false again. But we need to do Distill A from D, which requires Pulse A (which we have) and Essence D (which is true). So let\u0027s proceed.\n\nStep 4: Distill A from D.\n\nPrerequisites: Essence D (yes) and Pulse A (yes). So yes.\n\nAfter Distill A from D:\n\n- The following become true: Nexus, Essence A (the first object), and A harmonizes D (since the first object is A, harmonizes the second D).\n\n- The following become false: Essence D (since it\u0027s the other object) and Pulse A (the first object\u0027s pulse).\n\nSo after Distill:\n\n- Essence: A (from the result), C, B (since D\u0027s Essence is now false)\n- Aura: B, D (since D\u0027s Aura was still present? Wait, Aura isn\u0027t affected by Distill. Let me check the Distill effects again.\n\nWait, the Distill action\u0027s effects are:\n\n\"Once Distill action is performed the following will be true: Nexus, Essence object, Object Harmonizes other object.\n\nOnce Distill action is performed the following will be false: Essence other object, Pulse object.\"\n\nSo for Distill A from D:\n\n- True: Nexus (so global Nexus is true again), Essence A (so A\u0027s Essence is true again), and A harmonizes D.\n\n- False: Essence D (so D\u0027s Essence is now false), Pulse A (so Pulse A is false).\n\nAura is not mentioned, so Aura remains as before. So Aura D was still present (since we only set Essence D to false, not Aura). Wait, the initial Aura D was present, and in the steps before, when we did Divest and Silence, Aura D was still there. So after Distill, Aura D is still present unless changed. So Aura remains A (no, A\u0027s Aura was turned off by Illuminate, but after Distill, does it change? No, only the facts listed in the action\u0027s effects are changed. So Aura A is still false (from Illuminate), but others are as before except D\u0027s Essence.\n\nSo after Distill A from D:\n\n- Essence: A, C, B (since D\u0027s Essence is now false)\n- Aura: B, D, C (since A\u0027s Aura is still false)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse A: false\n- Harmonizes: A harmonizes D (new), and any others? No, since previous harmonizes were erased.\n\nNow, the goal requires A harmonizes D, which is done. Now we need B harmonizes C and D harmonizes B. Let\u0027s see.\n\nFirst, let\u0027s note that D\u0027s Essence is now false. So we can\u0027t use D in some actions unless we get its Essence back. Also, D\u0027s Aura is still present (since Aura wasn\u0027t touched here).\n\nLooking at the current state:\n\n- Essence: A, B, C\n- Aura: B, D, C\n- Nexus: true\n- Pulse A: false\n- Harmonizes: A-D\n\nWe need to get B harmonizes C and D harmonizes B. Let\u0027s see how to get those.\n\nTo get B harmonizes C, perhaps we can do a Distill of B from C. Let\u0027s see:\n\nDistill B from C requires:\n\n- Essence of the other object (C) must be true (yes)\n- Pulse of B must be true.\n\nTo get Pulse B, we can do Illuminate B. Let\u0027s see if that\u0027s possible.\n\nTo Illuminate B, we need Essence B (yes), Aura B (yes), and Nexus (yes). So yes.\n\nStep 5: Illuminate B.\n\nPrerequisites: Essence B (yes), Aura B (yes), Nexus (yes). So possible.\n\nAfter Illuminate B:\n\n- Pulse B becomes true\n- Essence B, Aura B, Nexus become false.\n\nSo now:\n\n- Essence: A, C (since B\u0027s Essence is now false)\n- Aura: D, C (B\u0027s Aura is now false)\n- Nexus: false\n- Pulse B: true\n- Harmonizes: A-D\n\nNow, with Pulse B, we can do Distill B from C.\n\nStep 6: Distill B from C.\n\nPrerequisites: Essence C (yes) and Pulse B (yes). So yes.\n\nAfter Distill B from C:\n\n- The following become true: Nexus, Essence B (the first object), and B harmonizes C (the second object).\n\n- The following become false: Essence C (since it\u0027s the other object), Pulse B (the first object\u0027s pulse).\n\nSo after Distill:\n\n- Essence: A, B (since C\u0027s Essence is now false)\n- Aura: D, C (Aura C is still present unless changed, but Distill doesn\u0027t affect Aura)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse B: false\n- Harmonizes: A-D, B-C.\n\nNow, we have B harmonizes C, which is part of the goal. Now we need D harmonizes B. \n\nTo get D harmonizes B, we need to have D harmonize B. Let\u0027s see how to do that. \n\nD\u0027s current state: Essence is false (from earlier steps), Aura is still present (since we haven\u0027t touched it). To get D harmonizes B, perhaps we can do a Distill of D from B? Let\u0027s see:\n\nDistill D from B requires:\n\n- Essence of the other object (B) must be true (yes, since Essence B is true now)\n- Pulse of D must be true.\n\nTo get Pulse D, we need to Illuminate D. Let\u0027s see if that\u0027s possible.\n\nTo Illuminate D, we need Essence D (currently false), Aura D (yes), and Nexus (yes). Since Essence D is false, we can\u0027t do that. So we need to get Essence D back.\n\nHow can we get Essence D back? Let\u0027s think. \n\nLooking at the actions, perhaps using Divest or Silence. \n\nAlternatively, maybe we can use Divest on another object. Let\u0027s see.\n\nAlternatively, perhaps we can do a Divest on A from D, but let\u0027s see.\n\nWait, currently, A has Essence (yes), Aura is false (from Illuminate A earlier). To do Divest on A from D, we need:\n\n- A harmonizes D (which is true)\n- Essence A (yes)\n- Nexus (yes).\n\nSo Divest A from D would be possible. Let\u0027s try that.\n\nStep 7: Divest A from D.\n\nPrerequisites: A harmonizes D (yes), Essence A (yes), Nexus (yes). So yes.\n\nAfter Divest A from D:\n\n- Pulse A becomes true\n- Essence D becomes true (since the other object is D)\n- The following become false: A harmonizes D, Essence A, Nexus.\n\nWait, the Divest action\u0027s effects:\n\n\"Once Divest action is performed the following will be true: Pulse object (A), Essence other object (D).\n\nOnce Divest action is performed the following will be false: Object Harmonizes other object (A harmonizes D), Essence object (A), Nexus.\"\n\nSo after Divest A from D:\n\n- Pulse A is true\n- Essence D is true\n- A no longer harmonizes D\n- Essence A is false\n- Nexus is false.\n\nHmm, but we wanted to keep A harmonizes D. That\u0027s a problem. Because the goal requires A harmonizes D. So this might not be the right path. Let\u0027s see if there\u0027s another way.\n\nAlternatively, perhaps we can get D\u0027s Essence back through another method. Let\u0027s think.\n\nAlternatively, after step 6, we have:\n\n- Essence: A (no, wait, after step 6, after Distill B from C, Essence B is set to true (from the Distill\u0027s effect). Wait, let me recheck step 6\u0027s effects.\n\nWait, in step 6, Distill B from C:\n\nThe Distill action\u0027s effect says \"Essence object\" (the first object, which is B) becomes true. So yes, Essence B is true. But what about Essence A? In step 5, when we did Illuminate B, we turned off Essence B, but then in step 6\u0027s Distill, we turned it back on. Wait, let me retrace:\n\nAfter step 5 (Illuminate B):\n\n- Essence B was turned off.\n\nThen step 6 (Distill B from C):\n\n- The Distill action\u0027s effect sets Essence B to true again. So yes, after step 6, Essence B is true again.\n\nSo in step 6\u0027s aftermath:\n\n- Essence: A (from step 4\u0027s Distill A from D, which set Essence A to true again?), wait let me retrace step 4\u0027s Distill A from D.\n\nStep 4: Distill A from D. The effect was \"Essence object (A) becomes true\". So yes, after step 4, Essence A is true. Then step 5 (Illuminate B) only affects B\u0027s Essence, so A\u0027s Essence remains true until step 7?\n\nWait, step 7 was Divest A from D, which would set Essence A to false. But if we don\u0027t do that, then in step 6\u0027s aftermath:\n\n- Essence A is still true (from step 4\u0027s Distill)\n- Essence B is true (from step 6\u0027s Distill)\n- Essence C is false (from step 6\u0027s Distill, since the other object was C, so Essence C is now false)\n- Essence D is false (from step 4\u0027s Distill, which set Essence D to false)\n\nWait, in step 4\u0027s Distill A from D, the other object is D, so Essence D is set to false. So D\u0027s Essence is off.\n\nSo to get D\u0027s Essence back, perhaps we can do a Divest on another object that involves D. Let\u0027s see.\n\nAlternatively, maybe we can do a Silence on D to get its Essence back. Wait, Silence requires Pulse D. To get Pulse D, we need to Illuminate D, but that requires Essence D (which is off). So that\u0027s a problem.\n\nAlternatively, perhaps we can do a Divest on D from another object. Let\u0027s see.\n\nWait, to do Divest D from something, we need that D harmonizes that object, and Essence D, and Nexus. But D\u0027s Essence is off, so that\u0027s not possible.\n\nHmm, tricky. Let\u0027s think of another approach.\n\nWe need D harmonizes B. To get that, perhaps we can do Distill D from B. For that, we need:\n\n- Essence B (which is true)\n- Pulse D (so need to get Pulse D)\n\nTo get Pulse D, we can do Illuminate D, but that requires Essence D (which is off). So unless we can get Essence D back, we can\u0027t do that.\n\nAlternatively, maybe we can get Essence D back via another action. Let\u0027s see.\n\nLooking back, after step 6, the state is:\n\n- Essence: A, B (since Essence C is false, D is false)\n- Aura: D, C (since B\u0027s Aura was turned off in step 5, but D\u0027s Aura is still there)\n- Nexus: true (from step 6\u0027s Distill)\n- Pulse B: false (from step 6\u0027s Distill)\n- Harmonizes: A-D (no, wait, after step 6, when we did Distill B from C, the A-D harmonize was still there? Wait, no. Wait, in step 6\u0027s Distill B from C, the only harmonize added is B-C. The A-D harmonize was from step 4\u0027s Distill, but does it stay?\n\nWait, the Distill B from C doesn\u0027t remove any harmonizes except those explicitly mentioned. The Divest actions remove harmonizes, but Distill only adds a new one. So after step 4\u0027s Distill A from D, A harmonizes D is true. Then step 6\u0027s Distill B from C adds B harmonizes C. So the harmonizes are A-D and B-C. So that\u0027s correct.\n\nNow, to get D harmonizes B, perhaps we can do a Divest on B from D? Wait, but D\u0027s Essence is off. Alternatively, maybe we can do a Divest on D from B, but that requires D harmonizes B, which we don\u0027t have yet. Hmm.\n\nAlternatively, maybe we can do a Divest on A from D again, but that would remove A-D harmonize, which we need. Not good.\n\nAlternatively, let\u0027s think of another path. Let\u0027s see if we can get D\u0027s Essence back through a Divest action involving another object.\n\nWait, perhaps we can do a Divest on C from B. Wait, but C\u0027s Essence is off (from step 6\u0027s Distill B from C, which set Essence C to false). So that\u0027s not possible.\n\nAlternatively, maybe we can do a Silence on D to get its Essence back. Wait, Silence requires Pulse D. To get Pulse D, we need to Illuminate D, but that requires Essence D (which is off). So that\u0027s a loop.\n\nHmm, maybe we need to backtrack and try a different approach.\n\nLet me think again. The problem requires D harmonizes B. To get that, perhaps we can do Distill D from B. To do that, we need:\n\n- Essence B (which is true)\n- Pulse D (so need to get Pulse D)\n\nTo get Pulse D, we can do Illuminate D, but that requires Essence D (which is off). So unless we can get Essence D back, we can\u0027t do that.\n\nAlternatively, maybe we can get Essence D back via a Divest action. Let\u0027s see.\n\nSuppose we do a Divest on A from D (even though it removes A-D harmonize). Let\u0027s see what happens.\n\nStep 7: Divest A from D (as before):\n\nPrerequisites: A harmonizes D (yes), Essence A (yes), Nexus (yes).\n\nAfter Divest:\n\n- Pulse A becomes true\n- Essence D becomes true (since other object is D)\n- A no longer harmonizes D\n- Essence A becomes false\n- Nexus becomes false.\n\nNow, after this, we have:\n\n- Essence: B (since A\u0027s is now false), D (now true)\n- Aura: D, C (since A\u0027s Aura was off, B\u0027s was off)\n- Nexus: false\n- Pulse A: true\n- Harmonizes: B-C (since A-D was removed)\n\nBut now, we lost A-D, which is part of the goal. So that\u0027s bad. But maybe we can fix it later.\n\nNow, with Essence D back, we can try to get D\u0027s Pulse.\n\nStep 8: Illuminate D.\n\nPrerequisites: Essence D (yes), Aura D (yes), Nexus (no, it\u0027s false). So can\u0027t do that.\n\nHmm, Nexus is false here. So that\u0027s a problem.\n\nAlternatively, maybe Silence an object to get Nexus back. Let\u0027s see.\n\nWe can Silence A (since it has Pulse A from step 7). Let\u0027s try that.\n\nStep 8: Silence A.\n\nPrerequisites: Pulse A (yes). After Silence:\n\n- Essence A, Aura A, Nexus become true.\n- Pulse A becomes false.\n\nSo after Silence A:\n\n- Essence: A (now true again), B, D\n- Aura: A (now true), B (still false?), D (yes), C (yes)\nWait, Silence A sets Essence A, Aura A, and Nexus to true. So Aura A is now true again.\n\n- Nexus is now true again.\n\nSo now, after step 8:\n\n- Essence: A, B, D\n- Aura: A, B (since Silence A restored Aura B?), no, wait, the Silence action on A only affects A\u0027s Essence, Aura, and the global Nexus. So Aura B was turned off in step 5 (Illuminate B), and hasn\u0027t been turned back on. So Aura B is still false. So Aura now is A, B (no, wait, Silence A only affects A\u0027s Aura. So Aura B remains false. So Aura is A, D, C.\n\nWait, let me clarify:\n\nAfter step 7 (Divest A from D):\n\nAura was D and C (since B\u0027s was off). Then step 8 (Silence A):\n\n- Silence A sets Essence A, Aura A, and Nexus to true. So Aura A is now true, but Aura B remains as it was (still false from step 5). So Aura now includes A, D, C.\n\nSo after step 8:\n\n- Essence: A (true again), B, D\n- Aura: A, D, C\n- Nexus: true\n- Pulse A: false (from Silence)\n- Harmonizes: B-C (since A-D was removed in step7)\n\nNow, with Essence D and Nexus, we can try to Illuminate D to get Pulse D.\n\nStep 9: Illuminate D.\n\nPrerequisites: Essence D (yes), Aura D (yes), Nexus (yes). So yes.\n\nAfter Illuminate D:\n\n- Pulse D becomes true\n- Essence D, Aura D, Nexus become false.\n\nSo now:\n\n- Essence: A, B (since D\u0027s Essence is now false)\n- Aura: A, C (since D\u0027s Aura is now false)\n- Nexus: false\n- Pulse D: true\n- Harmonizes: B-C\n\nNow, with Pulse D, we can do Distill D from B to get D harmonizes B.\n\nStep 10: Distill D from B.\n\nPrerequisites: Essence B (yes) and Pulse D (yes). So yes.\n\nAfter Distill D from B:\n\n- The following become true: Nexus, Essence D (the first object is D?), wait no. Wait, Distill D from B means the first object is D, the second is B.\n\nWait, Distill D from B requires:\n\n- Essence of the other object (B) must be true (yes)\n- Pulse of D (yes)\n\nAfter Distill D from B:\n\n- True: Nexus, Essence D (the first object, D), and D harmonizes B (the second object, B).\n\n- False: Essence B (since it\u0027s the other object), Pulse D (the first object\u0027s pulse).\n\nSo after this:\n\n- Essence: A, D (since B\u0027s Essence is now false)\n- Aura: A, C (since D\u0027s Aura was turned off in step9, and B\u0027s was already off)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse D: false\n- Harmonizes: B-C, D-B.\n\nNow, we have D harmonizes B (good), and B-C (good). But we lost A\u0027s harmonize with D (since we had to remove it earlier). So we need to get A harmonizes D back.\n\nHmm, so now the harmonizes are B-C and D-B, but A-D is gone. So we need to fix that.\n\nTo get A harmonizes D again, we can do Distill A from D again. Let\u0027s see.\n\nFirst, we need to get Pulse A. Let\u0027s see:\n\nCurrent state after step10:\n\n- Essence: A, D\n- Aura: A, C\n- Nexus: true\n- Pulse D: false\n- Pulse A: ?\n\nPulse A was turned off in step8 (Silence A), and hasn\u0027t been turned back on. So Pulse A is false.\n\nTo get Pulse A, we can Illuminate A again.\n\nStep 11: Illuminate A.\n\nPrerequisites: Essence A (yes), Aura A (yes), Nexus (yes). So yes.\n\nAfter Illuminate A:\n\n- Pulse A becomes true\n- Essence A, Aura A, Nexus become false.\n\nSo now:\n\n- Essence: D (since A\u0027s is now false)\n- Aura: C (since A\u0027s and D\u0027s are off)\n- Nexus: false\n- Pulse A: true\n- Harmonizes: B-C, D-B.\n\nNow, with Pulse A and Essence D (since D\u0027s Essence is still true?), wait, after step10\u0027s Distill D from B, Essence D was set to true (from the Distill\u0027s effect). So yes, Essence D is true.\n\nSo to do Distill A from D again:\n\nStep 12: Distill A from D.\n\nPrerequisites: Essence D (yes) and Pulse A (yes). So yes.\n\nAfter Distill A from D:\n\n- True: Nexus, Essence A (the first object), A harmonizes D (the second object D)\n- False: Essence D (since it\u0027s the other object), Pulse A (the first object\u0027s pulse)\n\nSo after this:\n\n- Essence: A (from Distill\u0027s effect), D is now false (since it\u0027s the other object)\n- Aura: C (since A\u0027s Aura was turned off in step11, D\u0027s was off)\n- Nexus: true (from Distill\u0027s effect)\n- Pulse A: false\n- Harmonizes: A-D (new), B-C, D-B (wait, does D-B still hold?)\n\nWait, the Distill A from D doesn\u0027t affect existing harmonizes unless they are explicitly removed. The only harmonize added is A-D. The existing B-C and D-B remain unless an action removes them. Since we didn\u0027t do any Divest that would remove them, they should still be there.\n\nSo now, after step12, the harmonizes are A-D, B-C, D-B. Which is exactly the goal!\n\nSo the final state meets all the goals. Let\u0027s check the steps again to make sure there are no errors.\n\nLet me recap the steps:\n\n1. Divest C from B \u2192 gets Pulse C, Essence B, loses C harmonizes B, loses Nexus, Essence C.\n2. Silence C \u2192 restores Essence C, Aura C, Nexus; Pulse C off.\n3. Illuminate A \u2192 gets Pulse A, loses Essence A, Aura A, Nexus.\n4. Distill A from D \u2192 gets A harmonizes D, Nexus, Essence A; loses Essence D, Pulse A.\n5. Illuminate B \u2192 gets Pulse B, loses Essence B, Aura B, Nexus.\n6. Distill B from C \u2192 gets B harmonizes C, Essence B, Nexus; loses Essence C, Pulse B.\n7. Divest A from D \u2192 removes A-D, gets Pulse A, Essence D; loses Essence A, Nexus.\n8. Silence A \u2192 restores Essence A, Aura A, Nexus; Pulse A off.\n9. Illuminate D \u2192 gets Pulse D, loses Essence D, Aura D, Nexus.\n10. Distill D from B \u2192 gets D harmonizes B, Essence D, Nexus; loses Essence B, Pulse D.\n11. Illuminate A \u2192 gets Pulse A, loses Essence A, Aura A, Nexus.\n12. Distill A from D \u2192 gets A harmonizes D, Essence A, Nexus; loses Essence D, Pulse A.\n\nWait, but in step 10, after Distill D from B, Essence B was set to false (since the other object is B, so Essence B becomes false). Then in step 11, when we Illuminate A, we need Essence A (which was restored in step8, but in step7 Divest A from D turned off Essence A, then step8 Silence A turned it back on. So yes, step11 can do Illuminate A.\n\nBut after step10, Essence B is false. So in step10\u0027s aftermath, Essence B is off. Then in step12, after Distill A from D, Essence D is off again. But the final harmonizes are all there.\n\nThis seems to work, but the path is quite long. Let me see if there\u0027s a shorter way.\n\nAlternatively, maybe there\u0027s a different sequence that avoids some steps. Let me think again.\n\nAlternative approach:\n\nStarting over, perhaps after getting A harmonizes D and B harmonizes C, we can find a way to get D harmonizes B without losing A-D.\n\nLet me try another path.\n\nStarting from the initial state:\n\nInitial:\n\n- Essence: A, C, D\n- Aura: A, B, D\n- Nexus: yes\n- Harmonizes: C-B\n\nGoal: A-D, B-C, D-B.\n\nFirst, let\u0027s try to get B-C first via Divest and Distill, then proceed.\n\nStep 1: Divest C from B (as before). Then Silence C, getting back Essence C, etc.\n\nThen, proceed to get A-D via Illuminate A, Distill A from D.\n\nThen, to get D-B, perhaps instead of going through the long path, let\u0027s see:\n\nAfter step 4 (Distill A from D), we have A-D, and Essence D is off. To get D-B, perhaps we can do:\n\nStep 5: Divest A from D (to get Essence D back and Pulse A, but lose A-D). Then Silence A to get back Essence A and Nexus.\n\nThen Illuminate D to get Pulse D, then Distill D from B (but need Essence B).\n\nWait, this is similar to the previous path. It might be necessary to go through those steps.\n\nAlternatively, after step 4 (Distill A from D), we have:\n\n- Essence: A, B, C (since Divest C from B gave Essence B, and Silence C restored Essence C)\nWait, no, let me retrace:\n\nWait, in the first path, after step4 (Distill A from D), the Essence D is off, but Essence B and C are present?\n\nHmm, perhaps there\u0027s a smarter way. Alternatively, maybe the initial plan is the way to go, even if it\u0027s long.\n\nAlternatively, let\u0027s see the example plans given. In the first example, the plan had Divest, Silence, Illuminate, Distill, etc. The second example had multiple Divest and Silence steps. So perhaps the solution requires multiple cycles of Divest, Silence, Illuminate, Distill.\n\nGiven that, the path I outlined earlier works, even if it\u0027s lengthy. Let me check if all steps are valid and the final state meets the goals.\n\nYes, in the final step (step12), the harmonizes are A-D, B-C, D-B, which is exactly the goal. The other facts like Essence and Aura might not matter as long as the harmonizes are there. The problem only specifies the goal as the harmonizes, so that\u0027s okay.\n\nTherefore, the plan would be the sequence of steps I outlined. Let me write them in order as per the required format.\n\u003c/think\u003e\n\n[PLAN]\ndivest Block C from Block B\nsilence Block C\nilluminate Block A\ndistill Block A from Block D\nilluminate Block B\ndistill Block B from Block C\ndivest Block A from Block D\nsilence Block A\nilluminate Block D\ndistill Block D from Block B\nilluminate Block A\ndistill Block A from Block D\n[PLAN END]",
    "instance_id": "4_1",
    "model_name": "Qwen/QwQ-32B",
    "query": "I am playing with a set of objects. Here are the actions I can do\n\n   Illuminate object\n   Divest object from another object\n   Silence object\n   Distill object from another object\n\nI have the following restrictions on my actions:\n    To perform Illuminate action, the following facts need to be true: Essence object, Aura object, Nexus.\n    Once Illuminate action is performed the following facts will be true: Pulse object.\n    Once Illuminate action is performed the following facts will be false: Essence object, Aura object, Nexus.\n    To perform Silence action, the following facts need to be true: Pulse object.\n    Once Silence action is performed the following facts will be true: Essence object, Aura object, Nexus.    \n    Once Silence action is performed the following facts will be false: Pulse object.\n    To perform Distill action, the following needs to be true: Essence other object, Pulse object.\n    Once Distill action is performed the following will be true: Nexus, Essence object, Object Harmonizes other object.\n    Once Distill action is performed the following will be false: Essence other object, Pulse object.\n    To perform Divest action, the following needs to be true: Object Harmonizes other object, Essence object, Nexus.\n    Once Divest action is performed the following will be true: Pulse object, Essence other object.\n    Once Divest action is performed the following will be false:, Object Harmonizes other object, Essence object, Nexus.\n\nHere is an example problem:\n\n[STATEMENT]\nAs initial conditions I have that, essence Block B, essence Block C, nexus, Block C harmonizes Block A, aura Block A, aura Block B.\nMy goal is to have that Block A harmonizes Block C and Block B harmonizes Block A.\n\nMy plan is as follows:\n\n[PLAN]\ndivest Block C from Block A\nsilence Block C\nilluminate Block A\ndistill Block A from Block C\nilluminate Block B\ndistill Block B from Block A\n[PLAN END]\n\nHere is another example:\n\n[STATEMENT]\nAs initial conditions I have that, essence Block B, nexus, Block A harmonizes Block D, Block B harmonizes Block C, Block C harmonizes Block A, aura Block D.\nMy goal is to have that Block C harmonizes Block D, Block A harmonizes Block C and Block B harmonizes Block A.\n\nMy plan is as follows:\n\n[PLAN]\ndivest Block B from Block C\nsilence Block B\ndivest Block C from Block A\nsilence Block C\ndivest Block A from Block D\nsilence Block A\nilluminate Block C\ndistill Block C from Block D\nilluminate Block A\ndistill Block A from Block C\nilluminate Block B\ndistill Block B from Block A\n[PLAN END]\nHere is the problem to solve:\n\n[STATEMENT]\nAs initial conditions I have that: aura Block A, aura Block B, aura Block D, essence Block A, essence Block C, essence Block D, Block C harmonizes Block B and nexus.\nMy goal is for the following to be true: Block A harmonizes Block D, Block B harmonizes Block C and Block D harmonizes Block B.\n\nMy plan is as follows:"
}

from datasets import load_dataset

ds = load_dataset("dmitriihook/qwq-32b-planning-mystery-16-24k-greedy", "default")

from datasets import load_dataset

ds = load_dataset("dmitriihook/qwq-32b-planning-mystery-16-24k-greedy")