Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'9', 1:'3', 2:'-', 3:'4', 4:'8', 5:'=', 6:'4', 7:'3']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [4, 6, 0, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


<gymnasium.vlm.groundtruth_interactor.MockVLM object at 0x1461e2780730>

Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'4', 1:'3', 2:'-', 3:'7', 4:'8', 5:'=', 6:'3', 7:'1']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 0, 1, 5])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'4', 2:'+', 3:'8', 4:'/', 5:'4', 6:'=', 7:'3', 8:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 1, 4, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'8', 2:'8', 3:'/', 4:'1', 5:'0', 6:'=', 7:'1', 8:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [8, 1, 5, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'/', 2:'1', 3:'5', 4:'=', 5:'3', 6:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 6, 1, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'8', 2:'/', 3:'5', 4:'=', 5:'9', 6:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 6, 2, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'8', 2:'+', 3:'6', 4:'9', 5:'=', 6:'3']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [2, 7, 6, 5])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'2', 2:'-', 3:'1', 4:'9', 5:'*', 6:'7', 7:'=', 8:'7', 9:'4', 10:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [8, 0, 2, 7])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'5', 2:'2', 3:'/', 4:'7', 5:'0', 6:'=', 7:'1', 8:'4']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [4, 0, 5, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'6', 2:'*', 3:'1', 4:'8', 5:'=', 6:'9', 7:'2', 8:'4']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 5, 1, 1])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'3', 1:'2', 2:'-', 3:'0', 4:'=', 5:'9', 6:'2']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [5, 5, 2, 7])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'+', 2:'2', 3:'*', 4:'7', 5:'=', 6:'2', 7:'7']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [7, 0, 0, 0])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'2', 2:'*', 3:'5', 4:'=', 5:'7', 6:'2']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 0, 3, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'6', 2:'/', 3:'7', 4:'9', 5:'=', 6:'3', 7:'0', 8:'4']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 0, 2, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'4', 1:'2', 2:'+', 3:'3', 4:'8', 5:'=', 6:'7', 7:'0']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [4, 1, 7, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'0', 2:'0', 3:'/', 4:'9', 5:'=', 6:'2', 7:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [7, 6, 1, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'2', 2:'+', 3:'7', 4:'4', 5:'=', 6:'7', 7:'4', 8:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 0, 8, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'9', 1:'4', 2:'-', 3:'5', 4:'6', 5:'=', 6:'9', 7:'0']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 5, 2, 7])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'3', 2:'+', 3:'5', 4:'=', 5:'1', 6:'7']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [2, 7, 3, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'9', 2:'5', 3:'/', 4:'1', 5:'4', 6:'=', 7:'1', 8:'4']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 0, 2, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'5', 1:'3', 2:'-', 3:'5', 4:'=', 5:'6', 6:'4']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [5, 4, 1, 5])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'3', 1:'2', 2:'+', 3:'9', 4:'5', 5:'=', 6:'1', 7:'3', 8:'7']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [8, 0, 4, 1])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'5', 1:'0', 2:'-', 3:'2', 4:'0', 5:'=', 6:'4', 7:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [7, 6, 0, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'5', 2:'+', 3:'7', 4:'0', 5:'=', 6:'3', 7:'6']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 0, 1, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'8', 2:'5', 3:'/', 4:'1', 5:'=', 6:'1', 7:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [1, 6, 4, 0])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'5', 2:'+', 3:'9', 4:'6', 5:'=', 6:'7', 7:'2', 8:'3']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 0, 4, 1])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'4', 2:'+', 3:'2', 4:'*', 5:'0', 6:'=', 7:'3', 8:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [8, 6, 5, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'9', 2:'-', 3:'5', 4:'0', 5:'=', 6:'7', 7:'2', 8:'9']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 0, 2, 7])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'3', 1:'7', 2:'+', 3:'9', 4:'9', 5:'=', 6:'7', 7:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 5, 4, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'0', 1:'+', 2:'4', 3:'*', 4:'6', 5:'=', 6:'9', 7:'2']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 5, 0, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'2', 1:'7', 2:'0', 3:'/', 4:'1', 5:'5', 6:'=', 7:'7', 8:'9']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [7, 0, 8, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'1', 2:'/', 3:'1', 4:'8', 5:'=', 6:'7', 7:'9', 8:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [6, 0, 2, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'2', 2:'8', 3:'/', 4:'1', 5:'8', 6:'=', 7:'1']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [2, 1, 7, 0])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'0', 2:'*', 3:'1', 4:'9', 5:'=', 6:'3', 7:'4', 8:'2']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 0, 1, 6])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'8', 2:'*', 3:'6', 4:'=', 5:'8', 6:'0']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [1, 6, 3, 1])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'0', 2:'*', 3:'7', 4:'9', 5:'=', 6:'1', 7:'3', 8:'0']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 0, 7, 5])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'6', 1:'9', 2:'+', 3:'2', 4:'7', 5:'=', 6:'8', 7:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 4, 1, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'8', 1:'+', 2:'7', 3:'*', 4:'9', 5:'=', 6:'6', 7:'3']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 1, 7, 5])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'1', 1:'2', 2:'/', 3:'1', 4:'9', 5:'=', 6:'1', 7:'5', 8:'6']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [4, 5, 2, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'0', 1:'+', 2:'1', 3:'0', 4:'/', 5:'3', 6:'=', 7:'9', 8:'0']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [7, 5, 4, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'8', 1:'0', 2:'+', 3:'1', 4:'2', 5:'=', 6:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [2, 7, 3, 0])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'5', 1:'4', 2:'+', 3:'1', 4:'=', 5:'4', 6:'7']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [2, 7, 3, 0])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'7', 1:'7', 2:'+', 3:'4', 4:'9', 5:'=', 6:'6', 7:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 0, 4, 4])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'6', 1:'5', 2:'+', 3:'0', 4:'=', 5:'8', 6:'5']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [2, 7, 0, 1])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'5', 1:'/', 2:'2', 3:'8', 4:'=', 5:'1', 6:'0', 7:'0']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [3, 6, 1, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>


Prompt:
You see an image of a broken matchstick equation.
Your goal is to fix the equation by moving ONE match per action.

Symbols (left→right) with indices:
[0:'8', 1:'/', 2:'8', 3:'=', 4:'4', 5:'8']

Available actions:
1. 'move': Remove one match from segment 'src_seg' of symbol at 'src_idx', then add it to segment 'dst_seg' of symbol at 'dst_idx'. Format: `('move', [src_idx, src_seg, dst_idx, dst_seg])` where:
   • src_idx, dst_idx ∈ [0, N−1], with src_idx ≠ dst_idx
   • src_seg, dst_seg ∈ matchstick_puzzles.TOTAL (e.g., {0..12})
   • The move must result in valid symbols at BOTH positions.
2. 'undo': Revert the last move (if any). Format: `('undo', 'undo')`
3. 'stop': Submit your current equation as final. Format: `('stop', 'stop')`

Success: The submitted equation must be mathematically correct (evaluated as lhs == rhs).

Segment legend (indices depend on symbol):
  0..6 : 7-seg digits (a,b,c,d,e,f,g)
  7    : plus vertical stroke (used by '+')
  8,9  : multiply diagonals (used by '*'); single {8} or {9} maps to '/'
  10   : diagonal for divide (if enabled in mapping)
  11,12: equals upper/lower bars (used by '=')
A segment is valid for a symbol only if the resulting set of segments maps to a known glyph.

Please respond with exactly one action and its arguments in the specified format. For example:
- To move a match: `('move', [0, 6, 2, 0])`
- To undo: `('undo', 'undo')`
- To stop: `('stop', 'stop')`

Verbalize your reasoning in <think>…</think> and give the final result in <answer>…</answer>.

Based on the current state, I need to take the optimal action to solve this task.<answer>('move', [0, 1, 1, 8])</answer>

Prompt: Environment feedback: Action executed successfully.

Based on the current state, I need to take the optimal action to solve this task.<answer>('stop', 'stop')</answer>