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

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


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

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

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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,F<2,Bv1,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,F<1,Cv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E>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: ooooooooooBoooooBooooCCCoooooDoooAAD
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<1,Bv1,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: oooBBBooooooooooooooAACoDDDoCoooooCo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
D^1,E<2,Dv2,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: oBoooooBoCoooooCDoAAoCDoEEEooooooooo
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: ooAABooooCBoDDDCBEFooGGEFHooooFHoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
H<3,Gv2,A>3
</answer>


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
D<2,Bv3,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: ooBCooAABCoooooCoooooooooooDDooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,B^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: ooBCCCoDBooEoDBooEoDoAAEoooooooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

<think>
Shortest path found.
</think>
<answer>
F<1,Ev3,A>3
</answer>


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
C<2,D<1,Bv3,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: oAAooBooCCCBDDooEEoooooooooFooGGoFoo
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: oBAACoDBooCEDooFFEGHHoIEGJJJIoGooKKK
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
K<1,Hv1,A>1
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F^1,G<2,Ev1,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: BoooCoBoDoCEBoDAAEFGHIIEFGHoJJFGoKKK
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
B<1,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: ooBBBooCAAoDoCoooDoCooEEooooooFFoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Bv2,A>4
</answer>


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
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: ooAABCoDoEBCoDoEBFGGGEoFoHHHIoJJJoIo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,Cv2,A>3
</answer>


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

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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<1,Dv1,Bv1,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: ooooooBCooDoBCooDoooAADEoFFFoEoooooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv2,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: ooooBooCCCBDAAooBDooooooooEEEooooooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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

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


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

<think>
Shortest path found.
</think>
<answer>
C^1,G>2,Cv2,A>4
</answer>


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
G<1,Dv1,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: oooooBoooooBAAoooBoCCoooooDDoooooEEE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

<think>
Shortest path found.
</think>
<answer>
E<3,Bv3,Cv3,A>3
</answer>


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,Cv1,A>2
</answer>


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
B<1,D^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: BBBooCoooooCooDAACooDoooooDoooEEooFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<1,F<1,Cv3,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: AAoBoCoooBoCoooBooooDDDooooEEEoooFFo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,D<2,Bv1,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,Bv1,A>3
</answer>


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
B<3,C^3,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: ooAABCoDooBCoDoEEooDoooFooGGHFIIIoHF
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,D<1,Bv2,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
F<2,Dv2,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: oooooooooooBoooCoBoAACoDoooCEDooooEo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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


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

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


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

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


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

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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,I<1,Dv2,A>3
</answer>


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,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: oooBoooAABoooooBoooooooCooDDDCoooEEC
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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

<think>
Shortest path found.
</think>
<answer>
D^1,Ev2,A>4
</answer>


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<2,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: oooooooBoooooBCoDEoBCoDEAAFooEooFooo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Fv1,Bv1,A>3
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
D<1,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: oBoooCoBoAACDBEooCDFEoooDFEGGGoFooHH
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Fv1,E>1,Bv2,A>3
</answer>


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv1,B<2,E^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: ooBoCDooBoCDoAAoCDoooooooEoooooEoooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,D<2,Bv1,A>4
</answer>


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

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


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

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

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

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


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

<think>
Shortest path found.
</think>
<answer>
Iv1,Dv1,A>2
</answer>


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
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: ooooBooAACBooooCooooDCEoooDoEoFFGGoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Ev1,Bv2,A>3
</answer>


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

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


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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
G<1,Dv2,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: ooAABoooooBoooooCoooooCoooDDCooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,D<1,Bv2,A>3
</answer>


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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