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

<think>
Shortest path found.
</think>
<answer>
C>1,E^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: BooCCCBDEEEFBDGGGFAAoooFoooHHHIIoJJJ
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: oooooooooooooooooBoAACoBoooCoooooCoo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
E<2,F<1,Cv3,A>4
</answer>


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
I<1,J<1,Ev2,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: ooooooooooooooooBoAAoCBooooCooooDDoo
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: AABoooooBoCCoDDoooEEFoooooFoGGooFooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F<1,G<1,Cv2,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: oBoooooBCoooAACoooooCDDDEFFoooEooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^1,Ev1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^1,Ev1,Ev1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,J^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: ooooBoooooBooooCCCoooDoEoooDoEoooAAE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Dv1,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: ooooBCooooBCAAooBDoooooDoooooDoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,Cv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
I<1,Ev1,Bv1,A>4
</answer>


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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E^1,F^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: oooooBoooooBooAAoBCooDDDCoooEECooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E<1,Bv3,A>2
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
D^2,G<1,Fv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Bv2,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,E<1,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Bv2,Ev1,Bv1,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B<2,D<2,E^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: oooooooBoooooBoCoooAACDoooooDoooooDo
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: ooBooCoDBAACEDFFooEDGoHHEoGoooooGIIo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv3,Cv2,C^2,A>3
</answer>


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv1,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: oooAABCCDooBoEDooBFEoGGGFHIJJJFHIooo
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: oBAACDoBEFCDoBEFooooEGGGHHHIIoJJooKK
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: ooAABoooooBoCDooEECDFooGoDFooGooFooG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<2,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F<2,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: oBBBoooCDooEoCDooEoCDFGooAAFGooHHFGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,G<1,I^1,A>2
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
F^1,Gv1,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: ooAABCDoooBCDEEEBCDooooooFFFooGGoHHH
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: ooooooBoooooBoCCCoBAAoDEooFFDEooooDE
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,C^3,A>4
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
I<1,Ev1,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Fv1,F<1,I<2,J<1,Dv3,A>4
</answer>


Board size: 6x6
Board: BCooooBCoDDDoAAoEooooFEoGGoFEooooFHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,H<3,Ev1,Ev1,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: BoooooBooCCCBoooooAAoDooEooDooEFFFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,E^1,F<1,Ev1,A>3
</answer>


Board size: 6x6
Board: oBoCCCDBooooDoEoFoooEoFoAAGHFoooGHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBoCAADBoCooDBEEooDoFFooGGoHIIoJJH
Optimal length (moves): 13
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,F<4,G<2,Bv3,H^1,J>1,Bv3,C<3,F^1,J<1,Gv1,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F>1,G<2,I^2,J<1,Ev1,A>2
</answer>


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

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


Board size: 6x6
Board: oooBBBoooooCoooooCDooooCDoooEFDAAoEF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBoooCCCoooDDDoooEFooAAEFoGGoEFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,D<1,Cv3,C>1,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: BBBooooooCCCAADooEoFDooEGFHIJKGFHIJK
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>3,D^2,A>3,Bv2,B<1,C<1,E^2,A>1
</answer>


Board size: 6x6
Board: ooBBBoCCCoDEFFFoDEoAAGDEoHHGIoJJoGIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BBBooCDooooCDAAooCoooooooooEEEooFFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoooCoBoooCDooAACDEooFFFEGGoooEooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,F<2,H<2,Cv3,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
C^1,F<2,Dv3,E>2,Bv2,A>4
</answer>


Board size: 6x6
Board: BoAACoBoooCoooDEEEooDFoGooDFoGoHHFoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBoCoooBoCoooAACoDooEEEDoFFFoDoGGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,F<1,G<1,Cv3,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>3,C<2,D^2,E<1,Bv2,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: oooAABCooooBCDDooBCEEFFFoooooooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AABCooooBCooooBDDDooooooEoooooEFFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>2,Bv3,C<3,Bv1,A>4
</answer>


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

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


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

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


Board size: 6x6
Board: oooBCoAAoBCooooBCooooDDooooEEEoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,E<3,Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: oooBoCDAABoCDooEECDoFFFoGGoHHHooIIoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E<2,F<2,Cv2,H<1,Cv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E<2,F<2,G<2,Cv2,Cv2,A>4
</answer>


Board size: 6x6
Board: AAoBooooCBooooCDooEEoDFoGHIIFoGHooFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,I>2,Ev1,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: BBBooooooAACooDooCEFDGGGEFDoHHEFoIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>3,D^2,G<1,Dv1,A>1
</answer>


Board size: 6x6
Board: oAABCDoooBCDoEEBoDFoGGooFoooHHFIIooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,G<1,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooBooCooBDoCAABDEFFoooEoGHHHEoGIII
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A<2,F>2,G^4,G<1,H<2,I<2,Dv3,A>4
</answer>


Board size: 6x6
Board: ooooooAAoBooCooBDDCEoBooFEGGGoFoHHHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C^2,E^1,F^2,G<2,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2,C^1,F<1,Cv1,A>1
</answer>


Board size: 6x6
Board: oooBoCDAABoCDooooCDoEEEoFFoGoooooGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,C^1,E<2,Cv2,A>3
</answer>


Board size: 6x6
Board: oAAoBooCooBooCooBooCoDDDoooooooEEoFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBoooAABoooooCDooEoCDooEFFDooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F<1,Dv2,Bv2,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: oooAABooCCoBDooEFFDooEGGoHHEIIooJJJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
J<2,Ev1,E<1,Bv1,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
G>2,I^2,J<1,Gv1,Bv1,A>3
</answer>


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

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


Board size: 6x6
Board: oooBBBooAACoDoEoCoDoEoFFDoGGGooooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Ev2,E<2,Cv1,A>2
</answer>


Board size: 6x6
Board: AAoooBoooooBooCDDBoECFFFoECooooEooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBAACDoBooCDEoFooDEoFGGGEHoIIooHooJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


Board size: 6x6
Board: oooBooooCBDoAACoDEoFooDEoFoGGooFoHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A>2,E^2,F^1,G<1,H<2,Ev2,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: oooBBBooAACoooooCooDoEFFoDoEooGGGEoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,A<1,E^3,F<2,Dv3,E>2,Cv2,A>3
</answer>


Board size: 6x6
Board: oooooooooooooooBoooooBoCAAoDECoooDEC
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoooooBoAAooBoCDEooFCDEooFCDGGGF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BooCCCBoDEEEBoDFFFGHDooIGHAAoIoHoJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Dv2,E<1,I^1,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F^1,J<1,Gv1,G<1,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBooCoooDoCEEEDoCAAFoGoooFoGoHHHoII
Optimal length (moves): 11
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,G^3,I<1,Ev3,E>3,F^2,A>3,Ev2,E<1,G^3,A>1
</answer>


Board size: 6x6
Board: ooooBoCDAABoCDEoBoCDEoFFoGHHoooGoIII
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,H>1,Ev2,E<4,G^2,H<1,Dv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^2,A>2,Bv2,C<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: ooBoooAABoooCCBDDooEFFFGHEooIGHoooIG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^3,G>1,Bv2,A>3,D^2,G<1,Cv2,A>1
</answer>


Board size: 6x6
Board: oooooBoooAABoooooBooCoDDEECFFFooCooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
B^1,E^2,F^1,G<3,Fv2,A>3
</answer>


Board size: 6x6
Board: oAABoCoooBoCoooDDCEEEoFFoGGGHoooIIHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,Bv1,F<1,Bv1,A>3
</answer>


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

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


Board size: 6x6
Board: oooooBoAAooBoooCCoooDEEEFFDoooooDooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,D^3,E<1,Cv2,A>1
</answer>


Board size: 6x6
Board: oAABoCoooBoCooDoEEFoDGHoFoDGHoFooGHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBCooDooCooDooCAADoooEoFFooEooooo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,B>1,C^1,A>3,Bv1,B<1,D^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: oBoooooBoCCCDoooEFDAAoEFooGGEFHHHooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
G^1,I>2,Bv3,D<2,Bv1,A>2
</answer>


Board size: 6x6
Board: oAABoCoDDBoCEEFFooGoHIIIGJHoKKGJHooo
Optimal length (moves): 12
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,D<1,F>1,H^3,I<1,K<1,Dv4,F>1,Cv1,H>1,Bv1,A>4
</answer>


Board size: 6x6
Board: oBBBoooooCCCDDDoooAAEooFooEooFooEooF
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,D>3,E^3,A>3,Bv3,B<1,C<1,D<1,F^3,A>1
</answer>


Board size: 6x6
Board: oBBBoooCCCoooAADoEoooDoEooFFoEGGGoHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBoCoooooCoDEFAAoDEFoooDoooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBCooAABCooDDBCEEEFFGoooHoGoIIHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
A<2,C^3,D<4,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: oooAABooCCoBDDoEoBFFFEGGooHHIoooooIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooooooooAAoBCooooBCoooooCooDDEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Fv1,F^1,I<1,J<1,Dv2,A>2
</answer>


Board size: 6x6
Board: ooBCCCooBDooAAoDooEFFFoGEooooGEooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,E^3,F<1,Ev2,A>3
</answer>


Board size: 6x6
Board: oAAoBoCDooBoCDoEEECFGGoHoFIIIHoFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BCoooDBCEFoDBCEFoooGEFHIoGJoHIAAJoHI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,H^1,I^1,J^1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv1,A>2,Bv2,C<2,F^1,A>2
</answer>


Board size: 6x6
Board: BBBCoooooCDEoAACDEoooFFFGHHHIIGoooJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^1,G^3,G<3,H<1,Cv3,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: oBoCCCoBoDoEoBoDoEAAFoGoHoFoGoHoooGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^2,A>2,Bv1,B<2,G^3,A>2
</answer>


Board size: 6x6
Board: oooooooBoooooBoCCCoAADoEoFoDoEoFoDoE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BoAACoBDEoCoFDEoGGFDHHHoFoooIIoJJKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>1,Ev2,F<2,Cv1,A>2
</answer>


Board size: 6x6
Board: ooooooooBoCoAABoCoDoooCoDooEEEooFFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,E<2,F<1,Cv2,A>4
</answer>


Board size: 6x6
Board: AABooCooBDDCEEBFoCGooFHHGooFIJooooIJ
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,C<3,E^2,F^2,Gv1,G<4,Bv1,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooBooooCBooDECFFFDEoAAGDEoooGHIIooGH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BooCDoBooCDEooAADEFFGGoooHIJJJoHIooo
Optimal length (moves): 11
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,G>2,F>2,H^4,A<2,G<2,I^4,I<2,J<2,Fv3,A>4
</answer>


Board size: 6x6
Board: ooooooBAACDoBEECDFGoHIoFGJHIoFGJHKKK
Optimal length (moves): 13
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,C^1,Dv2,D>2,F^1,G^1,J^1,K<3,Gv1,F>1,Hv1,Cv2,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: BoooCDBAAoCDBoooEEoFoGGoHFoIIIHJJKKo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<2,Dv2,G<1,Cv2,A>3
</answer>


Board size: 6x6
Board: BooCCCBDoEEEBDFFFGAAHooGooHIIIJJKKKo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,G^1,K>1,Hv1,A>4
</answer>


Board size: 6x6
Board: BBBooCAAoooCooooooDEFFGGDEHIIoDEHooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,A>2,E^3,F<1,G<1,Dv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv1,I>1,Dv2,E<1,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E>2,F^1,G<2,H<2,Dv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
G^2,H<1,I<1,Gv1,Bv1,A>2
</answer>


Board size: 6x6
Board: BoooooBooooCBAAooCoDDEoCooFEGGooFEoo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,D<1,F^4,A<2,F^2,G<3,Dv2,Dv2,A>3
</answer>


Board size: 6x6
Board: oooBBBooCCCooDDDEFAAooEFoGGooFoooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,C<1,E^1,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: ooooooooooooAAoBCooooBCooDDECoFFoEGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
A<2,C^1,D<3,Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: BooCCCBoooooBooDoooAADEooFFDEoGGHHEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooAABCooooBCDEEEFCDoGGFoHoIIIoHoooJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,I<1,Fv1,Bv1,A>2
</answer>


Board size: 6x6
Board: BBBooCoDoAACoDEooCoDEFFoGGGHIIoooHoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,D^1,E^1,F<2,H^2,I<1,Dv2,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>2,D>1,E^3,F<1,Dv1,A>1
</answer>


Board size: 6x6
Board: oBBBCoDoooCoDooEEEAAFGooooFGoooooGoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<1,Fv1,A>1,Dv2,D<3,F^3,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv2,E<1,Cv4,D>1,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: oooooooBBBoooCCCooooDEooAADEooooFFFo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoooAABoooooBoooooCCoDoEEEoDoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBoooAABoooooCDDoooCEEooFoooooFGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G<3,Cv2,Bv2,A>3
</answer>


Board size: 6x6
Board: ooooooooBCCCDoBoEoDAAoEFDoooEFoGGHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,A<1,G<1,Cv3,C<2,D^2,E^2,A>4
</answer>


Board size: 6x6
Board: ooBBBoooAACDooEECDFGoHHHFGoIIoFGJJJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^3,H<2,Dv1,Dv1,A>2
</answer>


Board size: 6x6
Board: ooBoCooDBoCooDBEEEoDAAoFoooGoFHHoGoF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Bv3,D<1,F^3,A>1
</answer>


Board size: 6x6
Board: oooBoooAABooooooooooCDDDooCoooooCooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,C^3,D<3,Cv4,C>3,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B^1,E^3,E<3,F^1,G^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: oooooBooooCBoAAoCBDEFFCoDEooooDEGGHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^1,E^1,G<2,H<2,Bv3,Bv2,A>2
</answer>


Board size: 6x6
Board: oooBBBoooooooooCCCAAoDEooFFDEooooDEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooAAoBoooCCBDEoooBDEFGGGHoFoIIHoFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


Board size: 6x6
Board: ooooooooBCCCooBDoEAABDoEoooooEooooFF
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B^1,Dv2,A>3,Bv2,B<1,D^2,A>1
</answer>


Board size: 6x6
Board: AAoBooCooBooCooDDDEoooooEoooFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
C>1,D^3,E<1,F<1,Cv1,A>2
</answer>


Board size: 6x6
Board: ooooooooooBoCDAABoCDEEBooDoFoooGGFHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,E<1,F^1,G<1,H<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: ooooooooBCCCooBooooAAoDoooEEDoooooDo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,E<2,Bv3,B<2,C^3,A>4
</answer>


Board size: 6x6
Board: BBBooooooCoooooCooooDEFoooDEFoAADEFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,G<1,H<1,Dv3,A>4
</answer>


Board size: 6x6
Board: BBBooCooooDCEoAADCEFFoDoEGooHHoGIIIo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,G^1,H<2,Cv3,I<1,Cv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F^2,G<1,Bv3,E<2,Bv1,A>4
</answer>


Board size: 6x6
Board: BoCCCoBoooooBooDDDooAAEFooooEFooooEF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


Board size: 6x6
Board: oooooBoCDoEBoCDoEooCDFFFAAoGoooooGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,F<3,G^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: ooBCCCooBDDDEFBooGEFAAoGoFoHHGIIIJJJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
A>1,F^2,G<1,H<1,Bv2,A>1
</answer>


Board size: 6x6
Board: BooCCCBooDoEBAADoEFFGGHooIIoHoJJoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev3,Gv1,F>2,Dv2,A>3
</answer>


Board size: 6x6
Board: BooCCCBooDoEAAoDoEFoGHHEFoGoIIooGJJJ
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Bv1,B<3,D^1,A>2,G^1,I<1,J<1,Ev2,A>1
</answer>


Board size: 6x6
Board: oAABCooooBCooDDBooEFFFGoEHooGoEHoIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBoooAABoooooBoooCCCoDDEEEFFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
G<2,Dv1,H<2,Cv2,Cv1,A>4
</answer>


Board size: 6x6
Board: BCAADoBCEEDoBFooDooFGGGoHHHooIoJJKKI
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>2,I^1,K>1,J>1,Fv2,F<1,Dv1,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: oooBooAAoBoooCCCDEoooFDEoGGFDoHHIIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,I>2,Fv1,Bv2,A>4
</answer>


Board size: 6x6
Board: oooBBBCCCDooAAoDEooFFFEoGHHHEoGooIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<3,D^1,I<2,Ev1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,C^2,D<3,E<3,Cv2,A>3
</answer>


Board size: 6x6
Board: oAABCooooBCoooooDoEFooDoEFoGGoEooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBBBCDooooCDEEEooFGooHoFGIoHAAGIoH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>1,G^1,I^1,A>3,Ev1,E<1,I^1,A>1
</answer>


Board size: 6x6
Board: oooooBAACooBooCDDDooCEoooFFEoooooEGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv2,C<1,Bv2,A>4
</answer>


Board size: 6x6
Board: ooAABoCooDBoCEEDBoFFGoHHooGIIIoJJKKK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
J<1,Gv1,G<2,Bv1,A>2
</answer>


Board size: 6x6
Board: oooBBBoooCCCoooooDoooooDooooEFoAAoEF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,E^1,F^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: oooooBoCAAoBoCoDDDoEEFFFoGGHHHIIIooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBooCCCBDoAAoBDooEEEDooFFFooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<1,F<1,Bv3,A>3
</answer>


Board size: 6x6
Board: ooooBCooooBCAAooBCDoEoFFDoEoooooEGGo
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,D^3,A<1,E^3,F<4,Ev3,G<3,Cv3,Cv3,A>4
</answer>


Board size: 6x6
Board: BCoDDDBCoEEEBCoFFFooAAoGHHIIoGooJJoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooAAoBCooDDBCEEFFFGGGooHooIIIHoJJJoH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoooCoBoAACoBoooDDDoooEEooooooFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<1,F<2,Cv3,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E^1,H<1,I<1,Gv2,Cv2,A>2
</answer>


Board size: 6x6
Board: oooBCoAAoBCoDooBCoDooEEEoooooooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<3,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: ooooBCDDDoBCooooBooooEEEAAFGoHooFGoH
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<3,G^3,F>3,G^2,A>3,Fv2,F<1,H^2,A>1
</answer>


Board size: 6x6
Board: AABCooooBCoooooCooDoEEEoDFFoooGGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
A>1,G^1,H<2,Cv3,Dv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F<1,Dv1,D<4,Bv2,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E^2,A>3,Dv1,D<1,F^2,A>1
</answer>


Board size: 6x6
Board: ooooBoooooBoAAooBooooooooCoDDDoCEEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBBBooooooCDAAooCDEoFFFDEGHIIIEGHJJo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D^1,A>3,F>1,H^3,G<1,I<1,Dv3,A>1
</answer>


Board size: 6x6
Board: oooooBoAAooBCDDooBCoEFFFooEGGGooEHHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,D>2,E^3,F<1,G<1,Cv2,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: AAoBoooCoBDDoCoBEoFGoHEoFGoHEIFGoJJI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I^1,J>1,Hv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oooBBBCoDDDoCoEEEoCoFoGHAAFoGHooIIJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBBBCoooooCoAAooCoooooDDooooEEooFFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<2,E<2,F<1,Cv3,A>4
</answer>


Board size: 6x6
Board: ooBoooAABooCooBDoCoooDoCEooDFFEooooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E^2,F<4,Bv2,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: BBBooCoDoAACoDEEoCFoooooFGGHHHIIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G<1,H<1,Cv2,A>1
</answer>


Board size: 6x6
Board: ooBooCoDBAACEDBFFFEoooooooGGoooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<2,Bv3,E<1,Bv2,A>1
</answer>


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

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


Board size: 6x6
Board: oBCooooBCoooooCDDDEoAAoFEGoooFoGHHII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,H<1,I<1,Gv1,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: BoooooBoooooBoCCCDooEooDAAEooDooEooo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,C>1,D^2,A>3,Cv2,C<1,E^2,A>1
</answer>


Board size: 6x6
Board: oBBBCoooAACDEFFFCDEGGHHoooIIIoJJKKLL
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D^1,G<1,H<1,I<1,Cv2,A>2
</answer>


Board size: 6x6
Board: oooooooBBBoooooooooooCooAADCEoooDCEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAABooCooBooCooDDDCooEEoFFFoGGoooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Cv2,C<3,Bv1,A>3
</answer>


Board size: 6x6
Board: BooCCCBoooooDooEooDAAEFoGGoEFoHHooFo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Dv1,Bv1,B<3,D^2,F^3,A>3
</answer>


Board size: 6x6
Board: ooooBCoAAoBCoooDoooEoDFFoEoDoooEoooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^2,F<2,Cv4,Cv4,D>2,Bv2,A>3
</answer>


Board size: 6x6
Board: ooooBoooAABoooooCCoooDEEoooDooFFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,Dv1,D<2,Bv2,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E^2,G^2,H<3,Ev3,Ev2,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: oAAoBoooCoBooDCoBooDoEEEFDoGooFHHGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BCooooBCoDDDoCooooooooEooAAoEoooooEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBBBoooCCCDoooEoDAAoEoDoooEFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAoBooCCoBoDoEEFFDoGHooIoGHJJIKKHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoCDDDBoCoAABEFoGGGEFHHHoEFIIoJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,F^1,G<1,I<1,J<2,Cv3,Ev1,A>2
</answer>


Board size: 6x6
Board: BoooCoBoAACoDEooCoDEoFFFDEoGGHoooooH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F<2,G<1,Dv2,A>2
</answer>


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

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


Board size: 6x6
Board: oooBBBoCoDDDoCEEEFoGooHFoGIoHoAAIoHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E<1,H^1,I^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: ooooBCoAAoBCooooDoEFooDoEFoooGEooHHG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,H<1,Cv2,Bv2,A>3
</answer>


Board size: 6x6
Board: AABooCooBoDCooBoDCoEEEooFoGGHoFoooHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>2,Bv1,A>3,C^1,E<1,Cv1,A>1
</answer>


Board size: 6x6
Board: oooBBBooooooCCCoooooDoooAADEooooDEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooBCCCAABooDooBooDEooFFDEGGHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,E^1,G<1,Bv2,A>4
</answer>


Board size: 6x6
Board: AAoBoooooBoCDEEFFCDooGGGoooooooHHooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Cv2,E>1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Bv2,Bv2,G^1,I<1,Bv1,A>4
</answer>


Board size: 6x6
Board: AAoBoooooBCCDEEEFFDoGGHoDIIJHKLLLJHK
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBoAAooBoCDEoBoCDEFFooDGGGoooooHH
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,C^1,D^2,G>1,Ev2,E<3,F^2,G<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: oooBoooooBCooAADCooooDCooEEEoooooFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E<1,Dv1,F<1,Cv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,D^2,E^1,G<3,Dv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D^1,A>1,E^1,G<1,Dv3,A>1
</answer>


Board size: 6x6
Board: ooooBoCCCoBooAADBoEEoDFFooGHHoooGooo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,D^2,G^2,H<3,Ev2,F<2,Cv3,A>4
</answer>


Board size: 6x6
Board: oooooBooAAoBooCCoBoooDDDoEEFFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooBBBoooooooCooDooCAADooCooDEEE
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>2,D^2,A>3,Bv1,B<1,D^1,A>1
</answer>


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

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


Board size: 6x6
Board: ooBBBCoAAooCooDEoCoFDEooGFDHHHGFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,D^1,H<1,Cv2,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: oooooBoAAooBCCDDoBEoFGGGEoFoHoEoFoHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,D>1,F^3,G<1,Cv2,A>1
</answer>


Board size: 6x6
Board: oooooooooooooooBBBooCooDAACooDooCEEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBCCCoDBooooDoooEoooAAEFooooEFGGoooF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,B<1,E^2,F^3,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>1,F^1,G<2,Dv2,Dv2,A>2
</answer>


Board size: 6x6
Board: ooooBoAAooBoooooBoooCDDoEoCoooEoCooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AAoBooCCoBooDoEFFFDoEGoooHHGIIoooGJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,C>1,D^2,H<1,Ev1,E<3,Cv1,A>3
</answer>


Board size: 6x6
Board: BooooCBooAACoDDooCoooooooEFGGGoEFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBCDDDoBCoooEoFFFGEHAAoGoHoIIGoHoJJJ
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,J<1,Gv1,F>1,Cv3,C<1,E<1,H^3,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: ooBBBoooCCCDAAooEDFFGGEooHHIEoJJoIKK
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C<2,D^1,E^2,G>2,I^4,H<2,K<2,Dv3,A>4
</answer>


Board size: 6x6
Board: oooooBooooCBooooCDAAoECDoooEFFGGGHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E^2,F<1,Ev2,A>4
</answer>


Board size: 6x6
Board: oooooooBoCCCoBooDEFoAADEFoooDoFooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<3,I^1,J^1,K^1,A>4
</answer>


Board size: 6x6
Board: BoooooBCCCooooDDDooooEoooAAEoooooEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv3,B<1,C<2,E^2,A>3
</answer>


Board size: 6x6
Board: oBAAoCoBooDCooooDCooEFFFooEoGGooEHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBooCCCBoooDooAAoDoEoFoooEoFoGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,D^1,G<1,Ev1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
I>1,Ev1,E<3,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: ooAAoBooCCoBDDoooEoFFGoEHHoGoEoooGII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^1,I<1,Fv1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooBoooooBooooooCooDoECooDFEGoAAFEGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBoCoooBoCAAoooCoooDDoEFFGGGEooHHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,E^2,F<1,G<1,H<1,Cv3,A>3
</answer>


Board size: 6x6
Board: BoooooBCCCoooAADEoFFoDEoooGoEoooGoHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,G^1,H<2,Dv1,A>3
</answer>


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

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


Board size: 6x6
Board: oooBBBAAoooCooDEoCoFDEGGoFHHIIoFooJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,F^2,H<1,Fv2,F<1,Dv1,A>2
</answer>


Board size: 6x6
Board: ooooooBoAAoCBoDDoCBEEEFFGooooHGooooH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
A<1,G^1,H<4,Ev2,Ev1,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: oBCDDDoBCooEoBAAFEGoooFHGoIIFHooJJJH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
J<1,Fv1,A>1,Cv1,C<1,E^1,A>1
</answer>


Board size: 6x6
Board: oBoooooBoCCCoBooDoAAooDoooooDoEEEoFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BBBCoDoEoCoDoEFAADooFGGGHHHoIIJJKKoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G<1,I<1,Dv3,A>1
</answer>


Board size: 6x6
Board: ooooBoCAAoBoCoDDooooEFFGooEHHGooEIIG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,A<1,C<2,D^3,E<3,Bv2,Bv2,A>4
</answer>


Board size: 6x6
Board: ooooooooooooAAoooBoooCoBDooCoBDooCEE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E<3,Bv1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,J^1,L<1,Iv1,Cv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
D<1,G^1,J<1,Iv1,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Fv1,Cv1,J>2,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: BBBoooAAooCDooooCDEoooCoEFFGGHEooooH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Dv1,E^2,F<1,G<1,Dv1,A>3
</answer>


Board size: 6x6
Board: ooAAoBCCoooBDEEEFFDGHIIooGHoJKoGHoJK
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBBBoCoooooCoooooCAADoooEEDFFoooDoGG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,B>2,D^3,A>3,Bv1,B<1,D^1,A>1
</answer>


Board size: 6x6
Board: AAoBCooDDBCoooEEFFooGooHIIGJJHoKKooH
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E<2,G^3,G<2,J<1,Dv3,F>2,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoAAoCBooDDCBoooECooooEFFGooEooG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E^2,F<3,Bv2,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoCoooBoCAAoBooDEooooDEoFFoDooGG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,A<1,E^3,F<2,G<2,Dv3,A>4
</answer>


Board size: 6x6
Board: AAoBCDoEEBCDFoGGGDFHIIoJFHoKKJoHooLL
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,F<2,Bv1,Bv1,L<1,Jv1,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
H^1,A>3,Ev1,E<1,H^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: oAAoBoCCooBoooDDBooEFoGGoEFoHHooFIII
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,D<2,Ev1,E^3,F<4,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oAAoBooCDoBooCDEEEFFooGGHHIIIJKKKooJ
Optimal length (moves): 14
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,D^1,E<1,G<1,J^4,F>1,J>1,Bv3,A>2,D^1,E<2,Cv1,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Ev2,E<3,Bv1,Bv1,Bv1,A>4
</answer>


Board size: 6x6
Board: ooooBoAAooBoooCDEEFoCDGGFHoDooFHoooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,C^2,F<3,Bv3,C<2,Bv2,A>4
</answer>


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

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


Board size: 6x6
Board: oooBBBoooCDoAAoCDoEFFFDoEoGoHHEoGoII
Optimal length (moves): 15
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,D^1,F>2,G^3,G<2,H<3,I<2,Cv3,B>2,C^1,A>1,E^3,F<1,Ev2,A>3
</answer>


Board size: 6x6
Board: BoooCoBAAoCoBooDCooooDoooooDEEFFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,E<3,Cv2,Cv1,A>3
</answer>


Board size: 6x6
Board: AAooBCDDDoBCoEEEBCoFFoGGoooHHooooIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,G<2,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: oBoooooBCoDoooCoDEoFCGDEoFHGIEAAHoIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,Dv2,E<2,Bv1,Bv1,A>3
</answer>


Board size: 6x6
Board: oooBoCAAoBDCooEBDCooEoDoooFFooGGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,F<1,Bv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
B<1,C<3,Dv2,D^2,E^3,A>4
</answer>


Board size: 6x6
Board: oBoCCCoBAAoDoBEEEDFGGGoDFHHHIIoJJJoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


Board size: 6x6
Board: BCoDDDBCoooEBooooEooooFoAAooFGooHHoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,E^1,F^1,G^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: ooAABoCCDDBoEFFGGoEHoIoJEHoIKJoooIKJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,F<1,Bv1,A>2
</answer>


Board size: 6x6
Board: oooooBoAAooBoooCoBoooCoooooCDDoEEooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<3,Bv2,Bv1,A>3
</answer>


Board size: 6x6
Board: ooooBoCAAoBDCoEEBDooFGGDooFHHHoIIooo
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E<2,I<1,Fv1,F<3,G^2,H<2,Cv2,Cv1,A>3
</answer>


Board size: 6x6
Board: oooBCoDooBCoDAABoEDoFFFEooGHHEIIGooo
Optimal length (moves): 14
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F>1,G^1,I>1,Ev2,A<1,F^3,A>1,F^3,G<3,Fv3,H<2,Dv3,A>3
</answer>


Board size: 6x6
Board: oooooooooooooBBBooooCDDDooCEooAAoEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BCCCoDBoEoFDBoEoFDoAAGFoHHHGIJKKoGIJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAoBooCooBooCDDDoEEoFGHoIoFGHoIoFGH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooBooCooBooCAABooooDDooEoFFFoEoGGG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,D<1,E^2,F<2,G<2,Cv3,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: oooBBBoooCDooAACDoEooCooEooFFFEooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^2,F<3,Dv2,Dv2,A>3
</answer>


Board size: 6x6
Board: BBBoCoAADoCoooDEEEooDoooooooooFFFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>3,Dv2,D<2,Cv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E<2,G^1,H<2,Bv3,Cv1,A>2
</answer>


Board size: 6x6
Board: AAooBCDDDoBCEEooBFooGGoFHHHIoFoooIJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,G<1,I^1,J<1,Fv1,Bv1,A>4
</answer>


Board size: 6x6
Board: oAABCooDoBCooDooEEooFFFGoHHooGoooooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<2,Bv3,D<2,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E^1,I<2,Fv1,F<1,Bv1,A>1
</answer>


Board size: 6x6
Board: BooooCBoAAoCBoDDDEFGoHHEFGoIIIFGoJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,J<1,Ev2,Cv2,A>2
</answer>


Board size: 6x6
Board: oooBBBooCCCooooDDDooAAEooFFFEoooooEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B<2,C<1,D<2,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: oBBBoooCoDDDoCoEooFAAEoGFHHIIGFoJJJG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D<1,F^1,G^3,I>1,J<2,Gv2,A>3
</answer>


Board size: 6x6
Board: BBBCoDoAACoDooooooEoFFGGEooooooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Cv4,F<1,Cv2,A>3
</answer>


Board size: 6x6
Board: oooAABoCoDoBoCoDEEoCoooFooGGoFoooooF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G<1,Dv2,D<1,Bv1,A>1
</answer>


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

<think>
Shortest path found.
</think>
<answer>
A>2,F^1,H<2,I<2,Dv2,A>2
</answer>


Board size: 6x6
Board: oBoooooBoCCCoBooooAAooDoooooDoooooDo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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