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: ooAABoCCDDBooEooFFoEooGGHEIIJoHoooJo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
D<2,Cv1,Bv2,A>3
</answer>


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

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


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

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


Board size: 6x6
Board: ooooooooooBooAAoBoooooBooooCCDoEEEoD
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: ooooBoAACoBoooCoBoooCDoooooDoooooDoo
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: ooooooooooooooooooooBoCDAABoCDooBoCD
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>


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: oAAoBCDEoFBCDEoFoCDGoFooHGIIJJHGooKK
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: ooBAACooBooCoDEEoCFDoGGGFDHIIIFoHooo
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: AAooBoooooBoCCoDEoFFFDEoGHHDEIGooooI
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: oooBBBoooCCCoooDEooooDEooAADoooooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Bv4,C<1,Bv1,A>4
</answer>


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

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


Board size: 6x6
Board: oAAoBoooooBoooooBooooCCCooooooDDDooo
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: AABoooCoBDDDCEEEooooFoGGHoFoooHoFIII
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: oAAoBoooooBoooooCooDDDCooooooooooEEE
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: oooooooooBBBooCCCoooAAoDoooooDEEoooD
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: oAABoooCCBDDooEEEoFGooHHFGIIIJFGoooJ
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,Ev1,Cv1,A>4
</answer>


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,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: oooBBBoooooCAAoooCoooooCDDoEEEoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,C^1,Dv1,A>4
</answer>


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

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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv3,Bv2,Bv2,A>4
</answer>


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

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


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

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


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

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

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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,F<1,Bv3,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
D<2,Fv1,Bv2,A>3
</answer>


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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

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

<think>
Shortest path found.
</think>
<answer>
D>1,E^1,Gv1,A>4
</answer>


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
I<1,Fv1,Bv1,A>3
</answer>


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

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


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

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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,G<1,Cv1,A>4
</answer>


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

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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,H<1,Dv2,A>4
</answer>


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

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


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

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


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

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


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

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

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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv3,C<1,Bv2,A>4
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
G<2,Ev2,A>3
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
Cv3,D<1,Cv2,A>4
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Fv1,F<2,Cv1,A>3
</answer>


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv2,E<2,Bv1,A>3
</answer>


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

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


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

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


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

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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Hv1,Dv1,A>1
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Fv1,H<2,Ev1,A>4
</answer>


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

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

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

<think>
Shortest path found.
</think>
<answer>
Hv1,Bv1,A>2
</answer>


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
B^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: oooBBBoooooooooCoDoAACoDoEEEoDFFoooo
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: oooooBooAAoBoCDDoBoCoEEooFoGGGoFoooo
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: AAoBooCCCBooDDoBoooEEEFFGGGHIooooHIo
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: oooBoooooBoooAABooooCCooDoooooDEEooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<2,Dv1,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: oooBBBCDoooECDFFFEoDAAoEoGGGHHoooooo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,F<2,Dv1,A>4
</answer>


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


Board size: 6x6
Board: oooBBBoooooCoooooCAAoooCoDDoooEEoooo
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: oooooBooooCBAAooCBoooooooooDoooooDoo
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: oooBBBooooooooCoooooCDoEoAADoEoooDoE
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: ooooooAAoooBoCCooBoDooEEoDoooooDoooo
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: ooBBBCooDDDCAAoooCoooooooooEEooooFFF
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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

<think>
Shortest path found.
</think>
<answer>
Cv1,C<1,Bv2,A>2
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
D^2,G<2,Cv3,A>3
</answer>


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,C<3,Bv1,A>4
</answer>


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

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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,C^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: oooAABoooooBCooDDDCoooEECoooFFooooGG
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooAAooBoooooBoooooBoooCCCooDDoo
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: oooooooooooBoAACoBoooCoDoEEooDFFoGGG
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: oooooooBoCooDBoCoEDAACoEoFoooooFoGGo
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: BBBooooCCCoooooDoooAADoooooooooooEEo
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: BooooCBDoooCBDAAoCEoooFFEooooooooGGo
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

<think>
Shortest path found.
</think>
<answer>
Fv1,Cv1,A>3
</answer>


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

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


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

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


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

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


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

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

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

<think>
Shortest path found.
</think>
<answer>
Gv1,Cv1,A>3
</answer>


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

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


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

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


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

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


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

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


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

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

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

<think>
Shortest path found.
</think>
<answer>
Dv3,Dv1,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,Bv2,A>4
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,C^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: BCAADoBCooDoBCEoDoFoEoGGFHooooFHIIoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,A>4
</answer>


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

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

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


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

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


Board size: 6x6
Board: oooooooooooBoooooBoAACoBoDoCEEoDoCFF
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: ooooooooAABCooooBCooooBCDDDooooooooo
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: BooCCCBoooooBAAooDEooooDEooooDEoooFF
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: ooAAoBoCCooBDDooEEoFFoooGGooHHoIIIJJ
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: oooBBBooCCCooooooooAADoooooDoooooDoo
Optimal length (moves): 4
Return only the <think> and <answer> blocks.

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv2,G<2,Bv2,A>4
</answer>


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

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

Board size: 6x6
Board: oooooBCAAooBCooooBoooDDDoEFooooEFGGG
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: oBoooooBoooCoBoooCooDooEAADooEoooFFo
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: oooBBBooooooCoooooCoooDECoooDEooAADE
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: oooBooooCBDoooCBDoAACoDooEEFGGoooFoo
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: ooooBoAACoBoooCooooooooooooooooooooo
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: ooooooBBBooooCoooooCDooEooDooEAADooE
Optimal length (moves): 3
Return only the <think> and <answer> blocks.

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


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

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


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

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

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