You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBCooAABCooooBCDDoEoooooEooFooEGGFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: ooooooooooBooAACBoDooCBEDooooEDFFFoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,B^2,A>3
</answer>


Board size: 6x6
Board: ooBooCooBooCAAooDEooooDEooooDooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Dv1,A>4
</answer>


Board size: 6x6
Board: ooooooBBBCoooAACDoooooDoooooDoEEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,Dv1,A>3
</answer>


Board size: 6x6
Board: BBBooCooAADCoooEDCoooEoooooooooooFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,A>2
</answer>


Board size: 6x6
Board: ooBoooooBoooAABooooCoDDDECooooECFFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Bv3,A>4
</answer>


Board size: 6x6
Board: ooBCCCAABoooooDDoooooooooooooooooEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooooooooooBBBCoooooCooAADCooooD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,D^2,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooBooCCCBoooDoBoooDoAAooDoEEEFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^1,A>4
</answer>


Board size: 6x6
Board: oooooooooBBBCCCooDoEAAoDoEooFDoEooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,D^2,A>2
</answer>


Board size: 6x6
Board: oooBoooooBooCAABDoCoooDooooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,C^2,A>3
</answer>


Board size: 6x6
Board: ooBoooCoBoooCDBoooCDoEoFoAAEoFoooEGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F^1,A>3
</answer>


Board size: 6x6
Board: AAoBCooooBCooooDCooEEDoooFGooHoFGIIH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Dv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BoAAoCBDDEoCoooEoCoFGoHHoFGooooFGIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Cv1,A>2
</answer>


Board size: 6x6
Board: oooBBBoooCoooooCooDoAAoEDooooEoooooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^3,A>2
</answer>


Board size: 6x6
Board: BBBoCoooooCoooooCoooDooEAADooEFFDooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E^2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBooCCCBAAoooBooooooDDoooooooEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv3,A>4
</answer>


Board size: 6x6
Board: ooBBBoooooCooAAoCoDEEFFFDooGGGDoHHoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^1,A>3
</answer>


Board size: 6x6
Board: ooooooooooBoAAoCBDoEECBDoooFoDoooFoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,B^2,Cv1,A>4
</answer>


Board size: 6x6
Board: oBBBoCDDDooCoooooCAAoEooFFFEoGoooEoG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^3,A>4
</answer>


Board size: 6x6
Board: BoAACoBoooCooooDEEoooDooFFoooooooGGG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<2,Cv1,A>2
</answer>


Board size: 6x6
Board: BooooCBDDDoCoAAooCoooEEEoooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv3,A>3
</answer>


Board size: 6x6
Board: ooAABCDDDoBCEEoooCoooFFFGGGoHHIIooJJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,F<1,Bv1,A>2
</answer>


Board size: 6x6
Board: ooAAoBCCCooBooDDEFGGooEFHIIoEoHJJJoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,Bv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAAooBooCooBDDCEEBooCoFFGGGHHHIIJJoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooBoooAABCoDEEoCoDoooCoDoFFFoGGGHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,F<1,Bv1,A>2
</answer>


Board size: 6x6
Board: BooooCBooAACoooooCDoooEEDFooooDFGGGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv2,A>1
</answer>


Board size: 6x6
Board: oooBBBooAACDooEoCDoFEoCDoFoGGooFHHHo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,G<1,Cv1,A>2
</answer>


Board size: 6x6
Board: AABooCooBooCDoBEoCDooEooDooEFFGGGoHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooAAoBoooooBoooCCDDoooooooEEEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D<2,Bv1,A>3
</answer>


Board size: 6x6
Board: oooooBoAAooBCCDDoBooEoFFooEoooooEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv2,A>3
</answer>


Board size: 6x6
Board: ooBoooooBoCooDDDCoEAAoCFEoGGoFooHHHF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F^3,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooBoooCDBoooCDooEoooAAEFoooooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F^2,A>3
</answer>


Board size: 6x6
Board: BooCCCBooooDBooooDoAAooDoooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,A>3
</answer>


Board size: 6x6
Board: AAoBoooooBCCooDDDoooooEFooooEFooooEF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv1,A>4
</answer>


Board size: 6x6
Board: AABoooCoBoDDCEEEooCoooFFoooGGGoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>2,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooooooBBBoooAACDooEFCDooEFooGGEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C^2,A>2
</answer>


Board size: 6x6
Board: BAACooBooCooBDEEoooDoooFooGooFooGooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>2,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBoCDDDBoCoooBoEoAAoFEGGGoFoooooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,E^3,A>3
</answer>


Board size: 6x6
Board: oooBBBooooooooCCCooooDoooooDoooAADoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BoooooBoooooooooCooooDCooAADoEoooDoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E^2,A>3
</answer>


Board size: 6x6
Board: ooBoooooBCooDDDCooooooEooAAFEooooFEo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E^2,F^2,A>3
</answer>


Board size: 6x6
Board: ooBoooAABooooCCCoooooooooooDDooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C>2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooBooAAoBooooooooCoDDDoCooooEoooooE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooAABoooooBoCCDDDoooEoFooGEoFooGEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D<1,Bv1,A>1
</answer>


Board size: 6x6
Board: ooBBBoooCCCoAAoDoEFooDoEFooooooGGHHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D^2,A>4
</answer>


Board size: 6x6
Board: oAABooooCBDEooCBDEoooFFFGGHIIIooHooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<3,Bv1,A>3
</answer>


Board size: 6x6
Board: oooBBBoooooooooooooAACoooooCoooooCoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,C^3,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BBBoooooAACooDDoCoooooCooooEEEooooFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Cv1,A>2
</answer>


Board size: 6x6
Board: BoAACoBoooCoBooDDEFFFooEoooGGGHHHIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv1,A>2
</answer>


Board size: 6x6
Board: oAAooBoooooBCoDDDBCoEEFFCGGHHHIIoJJJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F<1,Bv1,A>3
</answer>


Board size: 6x6
Board: BoooooBoooooBooooooooCCCoooDoooAADoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<3,D^1,A>3
</answer>


Board size: 6x6
Board: oooooBoooAABoooCCCooooooooDDooEEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>1
</answer>


Board size: 6x6
Board: oooooooooBooAACBooooCoooooooooooooDD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,A>4
</answer>


Board size: 6x6
Board: ooBBBCooDooCooDoEoooDFEooAAFEoGGoFoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F^2,A>3
</answer>


Board size: 6x6
Board: oooooooBBBoooooooCoooDoCEooDoFEooAAF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F^1,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooooooooooooBCDoAABCDoEoBFDoEooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,C^1,A>2
</answer>


Board size: 6x6
Board: AAoBCoDDoBCoEEEBCFoGGGoFHooIIIHoooJJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,G<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oBCDDDoBCooEoBCAAEFFoGGGHHHoIIooJJoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<1,E^1,A>1
</answer>


Board size: 6x6
Board: oBCooooBCDEooBCDEFGoAAEFGHHIoFJJoIoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F^2,A>2
</answer>


Board size: 6x6
Board: AABoooooBoooooCCCoooooooDoEoFFDoEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C>1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBoAAooBoooooBoooCCCoooooooDDEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>3
</answer>


Board size: 6x6
Board: oooBBBoAAooCoooDDCEEoFFFGGoHHoIIIoJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooooBooooCBooAACBooDoEoFoDoEoFoDoEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,B^1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBBBoAACoooooCDDDooEEooFoGGHoFoooHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Cv1,A>4
</answer>


Board size: 6x6
Board: oooooooooooooooBoCoAABoCoooBDoooooDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,C^1,A>3
</answer>


Board size: 6x6
Board: BCoAADBCEooDBFEGGGoFoHHHoFIIoooJJKKK
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,G<1,Ev1,A>1
</answer>


Board size: 6x6
Board: AAoBooCCoBoooooBoooDDDoEoooFFEoGGGoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBoooAABooCCoBooDDooooooEEooooFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv2,A>1
</answer>


Board size: 6x6
Board: ooooooooBoCoooBoCDoEAACDoEoFFDoEooGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,A>2
</answer>


Board size: 6x6
Board: oooooooooooooooooooooBCDAAoBCDooooCo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,D^1,A>4
</answer>


Board size: 6x6
Board: AAoooBCCCDDBoEEFoGHooFIGHJJJIGooooIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAoBooCCCBDDooEFFFooEGHHooEGIooooGIo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<3,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBoooooBooooCooDAACoEDooooEDooooEo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,E^3,A>4
</answer>


Board size: 6x6
Board: oooAABooCCoBoooDDDEoooFGEoooFGEoooFG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>1
</answer>


Board size: 6x6
Board: BoAAoCBoDDoCBEEooCoooFFFoGoHoooGoHoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv1,A>2
</answer>


Board size: 6x6
Board: BBBooCoooooCAAoDEooooDEFoGGoEFHHHooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,Ev1,A>4
</answer>


Board size: 6x6
Board: BCoooDBCoAADoooooDEEEFFooGooHHoGIIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Dv2,A>1
</answer>


Board size: 6x6
Board: ooBBBoooooCoooooCoooAACoooooDoooooDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^1,A>2
</answer>


Board size: 6x6
Board: oooooooooooooooBBBAACoDoooCoDoooEEEo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,E<1,Dv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBoooooBoooooBooooAACoDoooCoDEEECoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,D^2,A>3
</answer>


Board size: 6x6
Board: oooooooooooBooAACBDDEECFGGooHFooooHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,A>2
</answer>


Board size: 6x6
Board: oooAABCooooBCooooBDEoFFFDEoGGoDoHHHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>1
</answer>


Board size: 6x6
Board: oooooooooooooAAooBoooooBoCCooBoooDDD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>3
</answer>


Board size: 6x6
Board: oooBBBoooooCoooooCAAoooCooooDDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^1,A>4
</answer>


Board size: 6x6
Board: ooBBBooooCCCDEEEFoDGGGFHIoAAFHIJJJoH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,F^1,H^2,A>2
</answer>


Board size: 6x6
Board: AABCDoooBCDoooBCooEEoooooooFFFoGGGHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BooCooBooCDEBFooDEoFAADEGGGHHoIIoJJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBoCDooBoCDooooCEoAAFoEoooFGGGoHHooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,G<2,Fv2,A>4
</answer>


Board size: 6x6
Board: oBoCCCoBoDDDooAAoEFGoHoEFGIHoJFGIHoJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D<1,E^2,A>2
</answer>


Board size: 6x6
Board: oooBoooAABCoooooCooDDoCooEoooooEoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>3
</answer>


Board size: 6x6
Board: oAAoBoooooBoooooCCDDEEEooFFGGGHHoIII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv1,A>3
</answer>


Board size: 6x6
Board: oooBBBoooCCCooDDDooooEoooAAEoooooEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<3,D<2,E^2,A>3
</answer>


Board size: 6x6
Board: AAoBCooooBCooooDDDoEoFFFoEGGHHoEoooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBoooooooooooooAAoCDEEEoCDoFFFCD
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^3,D^3,A>3
</answer>


Board size: 6x6
Board: ooooooBoooCoBoAACooDDoCooooEEEoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Cv2,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBoooooBoooooCCCoAAooDoooooDoooEED
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^3,A>3
</answer>


Board size: 6x6
Board: oBooooCBoDDDCoEoooFoEGGGFooAAHoIIooH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,G<1,H^2,A>1
</answer>


Board size: 6x6
Board: BooCCCBoooDoBoooDoooEFFFAAEooGooEooG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^3,F<1,G^2,A>4
</answer>


Board size: 6x6
Board: oBBBoooAACDooooCDooooCooEEoooooooFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooBooCooBooCoooooDoooooDooAAoDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A>3
</answer>


Board size: 6x6
Board: ooBCDoAABCDooooCDoEoooooEoooooEooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooAAoBoooooBooCooBooCDoEEoCDooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E<2,Bv1,A>3
</answer>


Board size: 6x6
Board: BooCCCBooDooBAADoooEEoFFoooGoooHHGoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,B<3,D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooBooAAoBCDoooBCDoooooDoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,B^2,Cv1,A>4
</answer>


Board size: 6x6
Board: oAABCoooDBCoooDoCoooEEooooooFFoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooAABoCCCoBDoooEEDFGHHHDFGIooooGIoJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,A>2
</answer>


Board size: 6x6
Board: AABooCooBDoCooBDoooEEFFFoooooGoooooG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,E<1,Bv1,A>4
</answer>


Board size: 6x6
Board: AAoooBooCCoBoooooBooDEEEooDFFFooooGG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<1,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBCoooAACoooooCoooooDDDoooEEoooFFFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<3,E<2,Cv2,A>3
</answer>


Board size: 6x6
Board: oooBBBoooooooAAoCooDDDCEooooCEoooFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv1,A>3
</answer>


Board size: 6x6
Board: ooooooooooooBooooCBooDoCoAADoCoooDoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BoooCDBAAoCDBoooEEooFFooGHHIIoGooJJJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Cv2,Cv2,A>3
</answer>


Board size: 6x6
Board: ooooooBooCooBooCDoAAoCDoooooDooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,A>4
</answer>


Board size: 6x6
Board: BCoDooBCoDooBCoDoooAAEoooooEoFooGGGF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<2,Ev1,A>3
</answer>


Board size: 6x6
Board: ooooooooooooAAooBoooooBoCCCoBooooDDD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv1,A>4
</answer>


Board size: 6x6
Board: oBBBoooooooooCooDooCooDEoCAADEoooFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,A>2
</answer>


Board size: 6x6
Board: oBAACooBooCooBoDDEFoGGoEFHHHoEFooIII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv1,A>2
</answer>


Board size: 6x6
Board: ooBooooCBooooCooDEAAooDEoFGGDooFHHoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E^1,A>4
</answer>


Board size: 6x6
Board: ooooooAABoooooBoooooBCCCooDDoooEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBBBoooAACoooDoCoooDECoooFEGGHoFoooH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^2,H>1,Cv1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBBBooCCCooDEooAADEooooDEooooooooFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Dv2,A>1
</answer>


Board size: 6x6
Board: oooooooooooooooBCDEooBCDEoAACDEooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A>2
</answer>


Board size: 6x6
Board: oAAooBoooooBooooCCoooooooooDDDoEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv1,A>3
</answer>


Board size: 6x6
Board: BBBoCooAAoCooDooCooDoEEEFoGGooFooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<2,Cv2,A>3
</answer>


Board size: 6x6
Board: ooBBBooooCooAAoCoDoooCoDoooooDooEEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,E<1,Cv2,A>4
</answer>


Board size: 6x6
Board: oooooBAAoooBoooooooCoDDDoCEFFooCEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv2,A>4
</answer>


Board size: 6x6
Board: oAAoBCDDDoBCEoooBoEFFFooEGoHHHoGoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooBooAAoBooooCCooDDooooooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAoBCooooBCooooBDDooooEoooFoEoooFoEo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,C<2,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBooCoDAAoCEDoooCEoooooEooFFFoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv2,A>2
</answer>


Board size: 6x6
Board: oooAABCDEEEBCDoooBoDoFFFooGHHoIIGJJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>1
</answer>


Board size: 6x6
Board: oooooBoAAooBoooooBCCoDDDooEEoooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv2,A>3
</answer>


Board size: 6x6
Board: oooooBoCCCoBDDDooBAAoEoooooEFFoooEGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,E^3,A>4
</answer>


Board size: 6x6
Board: ooAAoBoooooBoCCoDDooooooEEoFFFoooGGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooBoooAABooooooCoooDDCEooooCEoooooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BoooooBoCCCooooDDDEooooFEoAAoFoooGGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,F^1,A>2
</answer>


Board size: 6x6
Board: oBBBCoAAooCooooDDDEEFooGooFooGHHFooG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Cv2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooooooooBoCoAABDCooooDoooooDo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,D^3,A>3
</answer>


Board size: 6x6
Board: ooooBoooAABoooooBooooCCCooDDoooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv2,A>2
</answer>


Board size: 6x6
Board: ooooooooAABoooooBoooooBoCoooDDCoooEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv1,A>2
</answer>


Board size: 6x6
Board: oooBooAAoBoooooooooooCCCoDooEEoDoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<3,Bv2,A>4
</answer>


Board size: 6x6
Board: ooBBBoooooooooooCoAAooCooDDECooFFEoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^2,A>4
</answer>


Board size: 6x6
Board: AABCooooBCooooooooooooooDEooooDEoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooooooooooooooBCAADoBCEEDoBCooDFFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,C^2,D^3,A>4
</answer>


Board size: 6x6
Board: ooBBBCoDoooCoDoooooDAAEoFFGoEoooGoEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^3,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooAABoooooBoooooBoooCCCooooDDDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv1,A>2
</answer>


Board size: 6x6
Board: AAoooBCCDDDBooooEEFFFoGHIIoJGHKKoJGH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBoooAABoooCoooooCoDDDooooooooEEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,C<3,Bv2,A>3
</answer>


Board size: 6x6
Board: BCCCooBooDooAAoDoEoooDoEFFoooGHHHooG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D^2,A>4
</answer>


Board size: 6x6
Board: oooooooooBoooooBoCAAoBoCoooooCoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,A>4
</answer>


Board size: 6x6
Board: AAoBooCCCBDDooEFGGHHEFoIooEFoIoooooI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,Bv1,A>4
</answer>


Board size: 6x6
Board: AAooBCDDDoBCEEEooCFFFGoooooGoooooGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoooooBoooCooDAACooDooCooDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBBBooooCDooooCDoAAoCDooooooooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^1,D^1,A>4
</answer>


Board size: 6x6
Board: ooAABCooooBCoooDoEFFoDoEoooDoEoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Ev1,Bv1,A>2
</answer>


Board size: 6x6
Board: ooAABCDDDoBCEooooCEFoGGGEFoHIooJJHIo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,G<1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooooooooBoooooBCDoAAoCDooEECooooFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^1,A>3
</answer>


Board size: 6x6
Board: AABCooooBCooDDBCooEEoooooooooooooFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAoBoCDDDBoCoooEEEFGGHHHFIJKKLoIJooL
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<3,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oAABCoDDoBCoooEBCooFEooooFoooooFoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: AAoBoooooBCooooBCoDDDEEoooooFFoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBoooooBCDEoooCDEAAoCDoFoGGGoFoHHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBBBCoDoAACEDoFFoEoGooHHoGIIoooGoJJJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<2,Cv2,Dv1,A>2
</answer>


Board size: 6x6
Board: ooAABooCooBooCooBooCoDDDEEEooooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<2,Cv1,A>2
</answer>


Board size: 6x6
Board: oAABoooooBoCoDEEFCGDooFoGDooFoGoHHoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<1,Bv1,A>3
</answer>


Board size: 6x6
Board: AAoBoooooBoooooCCCoooDDDoEEEoFoooooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<3,Bv1,A>4
</answer>


Board size: 6x6
Board: oooAABooCooBoDCooBoDoEEEFGGoooFooHHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,A>1
</answer>


Board size: 6x6
Board: oooBCoAAoBCoooooCoooooooDDoooooooEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooAABoCDEoBoCDEoBooDooooFooGGoF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oooBBBoooAACoooooCooooDDooEEoooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv1,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooooooAABooCooBooCooBooCooDDD
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<3,Cv1,A>3
</answer>


Board size: 6x6
Board: ooBAACDDBEoCoFBEoCGFoHHHGFIIIooJJJoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooBBBooooCooDAACoEDooCoEoooooEFFoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Dv1,A>3
</answer>


Board size: 6x6
Board: BooCCCBAAooDoEoFFDoEGGGDoooHHHIIIJJo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Dv1,A>3
</answer>


Board size: 6x6
Board: ooooooBoooooBoooooAACoDEooCoDEoooooE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,E^3,A>4
</answer>


Board size: 6x6
Board: oBBBooooooCDooEoCDAAEFooooEFoooGGooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,E^2,F^2,A>4
</answer>


Board size: 6x6
Board: oooBBBoooooooCCCooooAAoDoooooDoooEED
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,D^3,A>2
</answer>


Board size: 6x6
Board: oooBoCAAoBoCooooooDDDoooooEoooFFEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAAoBoooooBooCooDDoCooEEooFFFooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv1,A>3
</answer>


Board size: 6x6
Board: oAABCooooBCooooBooDooooEDooooEooFFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oooBBBCDDDooCEoFFFCEoooooEAAoGHHIIIG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,G^2,A>2
</answer>


Board size: 6x6
Board: ooAABCooooBCDDEEoCFGGGooFHHHIIFoJJJo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooooooooBoooooBCooAABCooooDDDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,A>3
</answer>


Board size: 6x6
Board: ooooBooCCCBooooDDDoooooEooAAoEoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E^1,A>2
</answer>


Board size: 6x6
Board: AAoBCoooDBCoooDBCooEDooooEFFoooEoGGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooooooBooooCBooAACBDDDooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooooooooooooBCCCooBoDoAAooDooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,C<2,D^1,A>4
</answer>


Board size: 6x6
Board: oBoCCCoBoDDDoBoooooooEEEooAAoFoooooF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F^2,A>2
</answer>


Board size: 6x6
Board: ooooBCoAAoBCoooDooEooDooEooDFFEoGGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,A>3
</answer>


Board size: 6x6
Board: oooBoooAABCoDooBCEDFFoCEGoooHHGooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<3,Bv2,Bv1,A>3
</answer>


Board size: 6x6
Board: oBCooDoBCAADEBCoFFEGoHHoEGIIIJKKoLLJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Dv2,A>1
</answer>


Board size: 6x6
Board: ooooBooAAoBoCDoEEFCDGooFooGooFooGHHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv2,A>3
</answer>


Board size: 6x6
Board: BoooooBCDoEoBCDoEFoCooGFooooGoooAAGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,G^1,A>2
</answer>


Board size: 6x6
Board: ooBCooooBCoooooDDDooooEoAAooEFoGGGEF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,E^2,F^2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oAABoCoooBoCoDoEEooDFGooHHFGooooFooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,D>1,Bv1,A>3
</answer>


Board size: 6x6
Board: BBBoCoDoAACoDooEEoDoFoooooFGGoooFoHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv2,A>2
</answer>


Board size: 6x6
Board: oBooCooBooCoooooooDooooEDooFoEAAoFoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F^1,A>4
</answer>


Board size: 6x6
Board: ooooooooooBCoAAoBCooDDBCoooEEEoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Bv2,Bv2,A>3
</answer>


Board size: 6x6
Board: ooooBoAAoCBoDDDCooooECooooEoFoGGEoFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBooCoDBooCEDBoooEDooFGEoooFGoAAoFG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G^1,A>3
</answer>


Board size: 6x6
Board: oBBBoooCDEEEoCDooooooooFooGAAFooGooF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<1,F^2,A>1
</answer>


Board size: 6x6
Board: oBBBooooAACoooDDCoEoooCFEooGGFoHHHoF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Cv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBoCCCoBoooooBooooDDDEoooooEFooAAEFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F^1,A>3
</answer>


Board size: 6x6
Board: ooooooooBCooooBCooAABCoooooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,A>4
</answer>


Board size: 6x6
Board: ooBoooAABoooooCCCoDDooEFooGGEFoHHoEF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C>1,Bv2,A>4
</answer>


Board size: 6x6
Board: ooAAoBoooooBoCoooDECoooDEoFoooEoFooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Bv1,A>2
</answer>


Board size: 6x6
Board: AAoBoooCoBDDoCoBEEFGGGHIFoJJHIoKKoHI
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,G<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBoooAABoooooBoCDEEEoCDooooCDooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,E<1,Cv2,A>1
</answer>


Board size: 6x6
Board: BoooCoBoAACoBoDDDooEFGoooEFGHHoEoGII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv2,A>2
</answer>


Board size: 6x6
Board: ooooooooAAoBoCoooBoCooDDooooooEEFFoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBoAACoBooDCooooDEFFGGGEHHHooEooIIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Cv1,A>1
</answer>


Board size: 6x6
Board: oooooBoCoooBoCoDoEAAoDoEoooDoooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,Ev2,A>4
</answer>


Board size: 6x6
Board: oooooooooooooAABoCoooBoCDooEECDooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooooBBBoooooooCDooEoCDAAEoCFFoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^2,A>1
</answer>


Board size: 6x6
Board: ooooBooAAoBCDDDooCoooooCEEoFFFoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,F<1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooooAAooBCooooBCooooBoooDoooooDooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBoooooCooDooCAADEoCooDEFooGGEFoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Dv2,A>1
</answer>


Board size: 6x6
Board: ooooooAAoBCooooBCooooBoooooooooooDDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: AAoBooCCCBoooDoEEEFDGoooFoGoHoFoGoHo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<3,Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBoooAABoCoooooCoDDDECooooEFFGGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv2,A>1
</answer>


Board size: 6x6
Board: oooBooCCCBoDoAAooDoooooDoEEEoooFFGGG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,G<1,Dv2,A>3
</answer>


Board size: 6x6
Board: BCCCooBDEEEFBDoooFGDHHHIGooooIGAAooI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,I^1,A>3
</answer>


Board size: 6x6
Board: BoooooBoooCoBooDCoAAoDCEFFFooEoooooE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,E^3,A>4
</answer>


Board size: 6x6
Board: oooBBBooooooooooooooooCoAAooCDooooCD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,A>4
</answer>


Board size: 6x6
Board: oooBBBooooooooooCoooooCDEEEFCDAAoFoD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,F^1,A>4
</answer>


Board size: 6x6
Board: AAoooBoCoDDBoCoooEFCoooEFooooEFooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBoooooBCCCDEBoooDEoFFFGEoAAHGoIIoH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,H^2,A>1
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBoooAABoCoooooCoooDDoooooooooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,D<2,Bv2,A>4
</answer>


Board size: 6x6
Board: BoAACDBEEECDBFFooooGoHHHoGoIoooGoIoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: oooooooooBoCoooBoCoAABoCoooDDDoEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,A>3
</answer>


Board size: 6x6
Board: BBBoCoooooCoooDoCoAADEoooFFEGooHHEGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^3,A>4
</answer>


Board size: 6x6
Board: ooooBooAAoBoooCCCoDEoFFGDEoHHGDIIooG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,F<1,Bv2,A>3
</answer>


Board size: 6x6
Board: AABoooooBCoooDDCEEoFoGoooFHGoooFHIII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBCooAABCooooBCooooooooDDDooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,D<1,Bv2,A>2
</answer>


Board size: 6x6
Board: BBBooooooCCCooAADoEoooDoEoooFoEoooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^2,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooooBoooooBoCAAoBoCDDoooCoooEEoooFFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,F<2,Bv3,A>3
</answer>


Board size: 6x6
Board: oooooBooCCCBoDDDooooooEooAAoEFooGGEF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,E^2,F^2,A>3
</answer>


Board size: 6x6
Board: ooooooooooooooBAACDoBEoCDFBEoCDFooGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooooooBooooCBooooCoooooDoooooDooAAoD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A>2
</answer>


Board size: 6x6
Board: BBBooooooCDoAAoCDoooEEDoooFoooooFooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,Dv2,A>4
</answer>


Board size: 6x6
Board: oAABoooooBCCoooDDDEEFFGHoIIoGHoJJJGH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<3,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooooooooooAABCooDDBCoooooCoooEEEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^2,E<1,Cv1,A>4
</answer>


Board size: 6x6
Board: ooooBoAAoCBooooCBoooDDDooEoooooEoooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv2,Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBBBoooCCCooAADoEEFFDGooHHHGIIIJJo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Dv1,A>2
</answer>


Board size: 6x6
Board: oooooooBoooooBooooooooCDAAooCDooooCD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,A>4
</answer>


Board size: 6x6
Board: ooAABoCCCoBoooooBoDoEEEoDoooooDooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,A>2
</answer>


Board size: 6x6
Board: ooooooBBBoCoooooCDAAooCDoooooDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,A>4
</answer>


Board size: 6x6
Board: oooooBCooAABCDDDooCoEEFFooGHHHooGooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F<1,Bv2,A>1
</answer>


Board size: 6x6
Board: ooooBoAAooBoooooCCooooooooooooDDDooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv2,A>4
</answer>


Board size: 6x6
Board: oBAACooBDDCooBooEEooooFoooooFooooGGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Cv1,A>2
</answer>


Board size: 6x6
Board: BoooooBoAAoCBooDoCoooDoEoooooEooFFoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Cv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAooBooCCoBoooDDBoEooFFoEoGGGoHHHIII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBAAooCoDEEoCFDoGGGFooHHoFoooIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Cv1,A>4
</answer>


Board size: 6x6
Board: oooBoooAABooooCDDDooCoooEEooFFoooGGG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<3,Bv2,A>3
</answer>


Board size: 6x6
Board: BoooCoBAAoCooooDDoEEoFFGoooooGoooooG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,F<1,Cv2,A>3
</answer>


Board size: 6x6
Board: ooooBooCCCBooAAoBoDoooEEDoooooDooFFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,F<2,Bv3,A>3
</answer>


Board size: 6x6
Board: BoCCCoBoooDoBEEEDoAAooDoFFGHooooGHII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,A>4
</answer>


Board size: 6x6
Board: oBBBooCooDDDCoAAEoFGGGEoFHHIIIoJJKKK
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,E^2,A>2
</answer>


Board size: 6x6
Board: BooCCCBooDEoAAoDEooooDFoooooFoooooFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Dv2,D^1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooBBBoCCCoDoooooDoAAooDEEoooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,D^1,A>3
</answer>


Board size: 6x6
Board: BoooCoBAAoCoooooooooDEEEooDooooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<2,Cv2,A>3
</answer>


Board size: 6x6
Board: AAoBooCCoBDDoEEEFFGGGHoIooJHKIooJHKI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,A>4
</answer>


Board size: 6x6
Board: AAooBCDDEoBCFoEoBoFooGoHFIIGoHooooJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oAAooBoCCCoBDDDooBEoFFGGEHoIIIoHoJJJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,G<1,Bv1,A>3
</answer>


Board size: 6x6
Board: BoooooBooCCCooooooooooDoooAADoooooDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^2,A>2
</answer>


Board size: 6x6
Board: ooooBoooooBCooAABCoooDoooooDoEoooDoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,B^1,A>2
</answer>


Board size: 6x6
Board: oooBooAAoBoooCoDDDoCooooECoFFFEoGGGo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<3,Bv2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooAAoBoooooBoooooBoooCCCoooDDooEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv1,A>2
</answer>


Board size: 6x6
Board: oBoCCCoBoooDoBEAADFFEoGHooEoGHooooGH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,A>1
</answer>


Board size: 6x6
Board: ooAABoCDooBECDFFFECGoooHIGJJJHIGoooH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,F<1,Cv1,A>2
</answer>


Board size: 6x6
Board: oooBBBoCoooooCoooooCAAoDooEooDooEooD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,D^3,A>2
</answer>


Board size: 6x6
Board: ooooooooooBooCCCBooDooBoEDooFoEDAAFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,F^1,A>2
</answer>


Board size: 6x6
Board: oooooBoooAABooooCCooooooooDoooooDooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>1
</answer>


Board size: 6x6
Board: AAooBCooDDBCEEEoFCGoooFoGooooHGIIIoH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Fv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoooooBooAAoBooooooooCCooDooEEED
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv3,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oBBBooooooooooCDooooCDooAACDEoooooEo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,E^2,A>4
</answer>


Board size: 6x6
Board: oooBooAAoBCoooooCoDoooCoDooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooBooAAoBooooooooooCCDDoooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>2
</answer>


Board size: 6x6
Board: ooooBoAAooBoooooBooooooooooCCooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>4
</answer>


Board size: 6x6
Board: ooooooooooooAABCoooDBCEEoDBCFooDooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooooooooooBBBoooooooAAooCooDDDC
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^2,A>3
</answer>


Board size: 6x6
Board: ooooooAABCooooBCoooDDCooooooEEoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,D<1,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBoCoDoooCoDEooCoDEoFoGoAAFoGHHHFoG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,G^2,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooBBBoooCCCDoAAoEDoFFFEDooooE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C<1,E^3,A>2
</answer>


Board size: 6x6
Board: AAoooBoooooBooooCCooooooooooooooDDoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv1,A>4
</answer>


Board size: 6x6
Board: oBoooooBooooooCoooooCDoEoooDoEoAADoE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,A>3
</answer>


Board size: 6x6
Board: AABoCoDoBoCoDoBoooEFooooEFoGGGEFHHII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooooooBoCoooBoCDDDBooEoFooGEoFooGAAF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<1,F^1,A>1
</answer>


Board size: 6x6
Board: BBBooooooooooooCCCAADoooooDEEoooDooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>3,D^3,A>4
</answer>


Board size: 6x6
Board: oBoooooBCDDDooCooooooooooAAEoFoooEoF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F^2,A>3
</answer>


Board size: 6x6
Board: oBoCoooBoCoDoBooEDooAAEDoooooooFFGGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,A>2
</answer>


Board size: 6x6
Board: ooooooAAooBoooCoBoooCDDDoooooooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,C<2,Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooBBBoooooooCooDEoCAADEoCoooE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,D^1,E^2,A>2
</answer>


Board size: 6x6
Board: oooooooAAoBooCCoBoooDDDooEEooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv1,A>3
</answer>


Board size: 6x6
Board: oBoooooBCDDDoBCooEoFCAAEoFGGoooooHHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Ev2,A>1
</answer>


Board size: 6x6
Board: BAACDoBooCDoBooCooEEoooooFGGHooFooHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,A>3
</answer>


Board size: 6x6
Board: oooooooooBBBooooooooAAoCDEEooCDFFFoC
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^3,A>2
</answer>


Board size: 6x6
Board: ooooBoooAABCooooBCoooooCooDoooooDoEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>2
</answer>


Board size: 6x6
Board: oAABoooooBooCooBooCoDDEoCoooEoooooEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oBBBooCCCoooDEFoGoDEFHGIJoFHGIJAAHoI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^1,I^1,A>3
</answer>


Board size: 6x6
Board: BCCCooBoooooAADooEFFDooEoGooHEoGooHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Dv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooooooooBBBooAAoCooDDoCoooooC
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BBBoooooooCoAAoDCEoFFDCEoooDoEoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,Cv1,A>4
</answer>


Board size: 6x6
Board: oooBoooAABoCDooooCDooooCoEEEoooooFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooooooooBooooCBooAACBooooCDDooooEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,A>3
</answer>


Board size: 6x6
Board: oooooooooBBBoooCCCDAAEooDooEFFDooGGG
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,C<3,E^2,A>3
</answer>


Board size: 6x6
Board: oooooooooooBAAoCoBoooCoooDDoooooEEEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,A>4
</answer>


Board size: 6x6
Board: oooooBooAACBooooCoooooooooDEEEooDooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv1,A>2
</answer>


Board size: 6x6
Board: AAoBoCoDDBoCooooooEoooooEoFFFoEoGGHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBooAAoBoCDDDBoCoooooCooEEEooFFooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,E<2,Bv2,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBoooooBCCCoooDooEEEDoAAFoDoooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,F^2,A>2
</answer>


Board size: 6x6
Board: BCCCooBooDDDBEAAFooEooFGHoIIJGHKKKJG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,F^2,A>2
</answer>


Board size: 6x6
Board: ooooBoooAABoooooBooCoooooCooDDooEEEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv2,A>2
</answer>


Board size: 6x6
Board: oooAABoCCCoBoDEEoBFDooGGFHoIIoFHJJoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Bv1,A>1
</answer>


Board size: 6x6
Board: oooooBAAoooBoCCooBoooDDDooEoooooEoFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv2,A>4
</answer>


Board size: 6x6
Board: oooooooooBBBoooooCoDAAoCoDoooCoDoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^2,A>2
</answer>


Board size: 6x6
Board: BBBooooooooooooooooAAoCDoEooCDoEooCD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^3,D^3,A>3
</answer>


Board size: 6x6
Board: ooooooooooBoooAABoooooBoooooCCDDoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv2,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooBoooooBAACDEFFGCDEooGCDHHHGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: oAABoooooBoCoDDBoCEFoGoCEFoGooEFooHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oBBBoCoooooCoooAACDooEEEDooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv3,A>1
</answer>


Board size: 6x6
Board: oooBBBoooCCCoooooooooDooEAADooEFFDoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<3,D^2,A>3
</answer>


Board size: 6x6
Board: ooooooooBooCooBooCAABooCDDDooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,A>4
</answer>


Board size: 6x6
Board: oooooooooBBBoCoooooCoooooCooDEoAAoDE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,A>3
</answer>


Board size: 6x6
Board: oBoooCoBAAoCoBoDDDooooEoooooEooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Cv2,A>2
</answer>


Board size: 6x6
Board: AAoBCoDDDBCoooEBoFooEoGFHHIIGJooooGJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BooCCCBooooDooEEEDooAAoDoooFGGoooFoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,A>2
</answer>


Board size: 6x6
Board: ooooBoooAABooooCCCDDEoooFoEGGGFoEHHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv2,A>2
</answer>


Board size: 6x6
Board: BooCCCBooooDBEoooDoEAAoDoooFFoGGoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: oooBBBooCoDoooCoDEoAAooEFFoooEoGGoHH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,E^2,A>3
</answer>


Board size: 6x6
Board: oooBoooooBooAAoBooCoDDoECoFooEooFooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,Bv3,A>4
</answer>


Board size: 6x6
Board: BBBoooooooooooooooAACoDoEECoDooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,A>4
</answer>


Board size: 6x6
Board: oooooBCoAAoBCDDoooEEoooFGHHHIFGoJJIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,Bv2,A>2
</answer>


Board size: 6x6
Board: oooBBBooooCoooooCDoAAoCDoooooDoooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^1,D^2,A>3
</answer>


Board size: 6x6
Board: oooooooBooCooBooCooBDECFooDEoFAADEoF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,F^1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: AAoBCooooBCooooBCoooooooDDDoooEEoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBoooooBoooooCCCooooDoEoooDoEoAADo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^1,A>2
</answer>


Board size: 6x6
Board: BBBoooooooooooooCDAAooCDoooooDooEEEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,A>4
</answer>


Board size: 6x6
Board: oAAoBoooooBooooCCCoooooooDoooooDoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv1,A>3
</answer>


Board size: 6x6
Board: oooooooAABoooCoBDDECoBooEoFFooEooGGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,A>3
</answer>


Board size: 6x6
Board: BoooooBoAAoCoooooCDDooEEoooFFFoooGGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv1,A>2
</answer>


Board size: 6x6
Board: oooooBoooAABooooCCoDooEEoDoooooDooFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,E<1,Bv2,A>1
</answer>


Board size: 6x6
Board: ooAAoBCCCooBoooooDoooooDoEEooDoooFFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Dv1,Bv1,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooBAAoooBoooooBooCDDDEoCoooEooFFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<1,Bv2,A>4
</answer>


Board size: 6x6
Board: BBBoooooAACDoooECDFooECoFGGEoHFIIIoH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,A>2
</answer>


Board size: 6x6
Board: ooBoooooBCooooBCDooooCDoEEEFDoAAoFoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F^1,A>4
</answer>


Board size: 6x6
Board: ooBoooAABoooooBooooCCDDoooooEEoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>4
</answer>


Board size: 6x6
Board: ooBoooAABoooCCDDDoEEoooooooFFFooGGoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D>1,Bv2,A>4
</answer>


Board size: 6x6
Board: BoooooBooCCCBDDDoooooooEoAAooEoooooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,E^2,A>3
</answer>


Board size: 6x6
Board: BCoDDDBCoooEBCFFFEGooAAEGooHHHGoIIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E^1,A>1
</answer>


Board size: 6x6
Board: BoooooBoooCoDoAACoDoooCoDoEEEooooFFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,F<1,Cv2,A>2
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: ooBBBoooCCCoDDDoooAAoEooooFEGGooFEoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C<2,E^3,A>4
</answer>


Board size: 6x6
Board: oooooBooAAoBoooooBCDoEEECDooooCDoFFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv2,A>2
</answer>


Board size: 6x6
Board: oooooooooBoooAABoCoDDBoCoooooEoooooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,B^2,A>3
</answer>


Board size: 6x6
Board: BoooooBoooooBooCCCoooDEFoooDEFAAooEF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,E^1,F^1,A>4
</answer>


Board size: 6x6
Board: oooBoooooBoooooCCCoooooDoooooDoAAooD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,A>3
</answer>


Board size: 6x6
Board: BBBoooooAAoCDoEEECDFoooCoFooGGoFHHII
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Cv1,A>2
</answer>


Board size: 6x6
Board: oAAooBoooooBoooCCCDoEFFoDoEoooDoEoGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv1,A>3
</answer>


Board size: 6x6
Board: BooCooBAACDoEoFCDGEHFoDGoHFooIoHJJJI
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooBBBoooAACoDEooCoDEooCFFEooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C^2,A>3
</answer>


Board size: 6x6
Board: ooooBoAAooBCoDDDBCoooooCoooEEEooooFF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Bv2,Bv1,A>4
</answer>


Board size: 6x6
Board: oooooooAAoBooCCoBoooooDoooooDooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oAAooBCCDDoBoooooEoooFGEHIIFGoHJJFKK
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooooooooooooooooAABooCDoBooCDoBooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^3,C^2,A>4
</answer>


Board size: 6x6
Board: AAooBoooooBoooooCoooooCoooooCoooDDoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoooooBooooCCCooAAoDEEoooDFFFooD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^3,A>2
</answer>


Board size: 6x6
Board: BoooooBooCDoEooCDoEAACDoooooFFoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BooAACBooDDCBooEEEooooooooooFoooooFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Cv1,A>1
</answer>


Board size: 6x6
Board: ooAAoBoooCCBoooooBoooooDooEEoDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooooooooooooBBBoooooCoooAACoooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C^1,A>3
</answer>


Board size: 6x6
Board: oooBBBAAooCDEoFFCDEGoooDoGooHoIIooHo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,A>4
</answer>


Board size: 6x6
Board: ooooBCAAooBCooooBooooooooooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooBBBCCCDDDoEEEooFoooGHFoooGHFoAAGH
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,H^1,A>2
</answer>


Board size: 6x6
Board: ooooBoCoAABoCoooBoCDEEEooDoooooDoooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^3,E<1,Cv2,A>2
</answer>


Board size: 6x6
Board: oAAoBCDEEoBCDFFGBCDoHGIoooHGIJoooooJ
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Iv1,Bv1,A>3
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: BBBCCCoDEoFGoDEoFGoooHoooooHIJAAooIJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I^1,J^1,A>4
</answer>


Board size: 6x6
Board: oooooooooBoooooBCoooooCoAADoCoEEDFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^2,A>4
</answer>


Board size: 6x6
Board: oAAooBCoDDoBCooooBCooEEEoooooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooBoooCoBoDoCoooDoEFFFDoEooGoooAAGoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,G^1,A>3
</answer>


Board size: 6x6
Board: oooooooooooBoAAooBoooooBoooCCCoooDDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,Bv2,A>3
</answer>


Board size: 6x6
Board: BBBooooCCCooooDDDoooAAEoooooEoooooEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E^3,A>2
</answer>


Board size: 6x6
Board: oooooooooBBBooooCoooAACoDoooCoDEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^2,A>2
</answer>


Board size: 6x6
Board: ooooooAAoBoooooBoooooCCooooooooooDDo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Bv1,A>4
</answer>


You are an expert Rush Hour (6×6) solver.

Input: 36-char row-major board; 'o' empty, 'A' red 2-long horizontal, others B..Z (len 2/3; H/V).
Output exactly ONE optimal solution wrapped in tags:
<think>
(brief internal reasoning)
</think>
<answer>
comma,separated,move,list
</answer>
Token format: <PIECE><DIR><STEPS> (A>2,B<1,Cv3). One move = slide any positive distance along axis.
Goal: right end of 'A' reaches the right edge.

Board size: 6x6
Board: oooooooooooooooooooooBBBoAAoCoDDooCo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C^2,A>3
</answer>


Board size: 6x6
Board: oooooooBoooooBooooooooCoAAoDCEoFFDCE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^2,D^2,E^2,A>4
</answer>


Board size: 6x6
Board: ooooBoCoooBoCooDDDCoEFoGoHEFoGoHoAAG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,G^1,A>1
</answer>


Board size: 6x6
Board: oooBBBoooCCCoooooDoooooDAAoEFooooEFo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F^2,A>4
</answer>


Board size: 6x6
Board: ooooooooooooBBBoooooCoooAACooooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>3,C^1,A>4
</answer>


Board size: 6x6
Board: ooooooooBoooAABooCoooDECoooDEooooDEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^2,A>4
</answer>


Board size: 6x6
Board: ooAABCoDDDBCooEEBCoFFFooGGoHHooIIIJJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Bv1,A>2
</answer>