Board size: 5x5
Board: AABoCooBoCDDoEEFoGGoFooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Bv3,D<1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BoooCBAADCoooDCEooFFEooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<2,Dv1,G<1,Cv2,A>2
</answer>


Board size: 5x5
Board: ooBBBooCDEAACDEFFGGooooHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCoDoBCoDEEoFFoooooGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,F>2,Cv2,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCDEoBCDEoFFoGGooooooHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Bv3,E<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAooBoCCoBooDEEoFDoGoFHHG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooCoBoDCoEEDFFFoDGGoHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,G>1,Cv2,D<2,Bv1,A>3
</answer>


Board size: 5x5
Board: AAoBCDEEBCDoFGGDoFooooHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<2,Fv1,F<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCDoEBCDoEoCooFFFoGGHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBBBooCAADoCooDoCEEEFFoGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDEoBCDEFFCGooHHGIIIo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Cv1,I>1,Dv2,E<1,Bv1,A>2
</answer>


Board size: 5x5
Board: oAAoBCDDoBCEooBoEFGGooFHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCoAABCooDDCEEooooFFGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABCCCoBDEEEBDFFGGDoooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDDDBCoEEFGHoIFGHoIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooooBCDDDBCoEooooEooAAEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCooBDCoEBDCFEGGoFHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABooCCBDoEFFDoEooGGEHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDooBCDEEFoGooFoGoHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBoDoCBoDEEFFFooooGGG
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBooCDDDoCAAEFFGoEooGHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
B>1,C^1,A<2,G^1,H<3,Ev1,Ev1,A>3
</answer>


Board size: 5x5
Board: BAACoBooCDBEFFDGEoooGHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBooooBooDEoAADEFFoDo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBooAABoCooBoCDDDEooFFE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBoECDBoEFoGGEFoooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,H<2,Fv1,Cv1,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABCDEEBCDooFFoGGoHHIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDoBCoDEoFoDEoFooEGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,E^1,G<2,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCDDDBCoEoFFoEooGoHHoG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoDoBCEDFGCEDFGoooFHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,F^1,H<2,Gv1,Bv1,A>2
</answer>


Board size: 5x5
Board: AABCDEEBCDFFooGHIoJGHIoJo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCDoBoCDEEoFGGoHFIIIH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,H^1,I>1,Dv2,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: oBBBoAAooCDEooCDEFFCDEGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBoDDCBEFFFoEGGoHHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BAAoCBDDDCEoFFGEHHoGoIIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,J<1,Gv1,Cv1,A>2
</answer>


Board size: 5x5
Board: BCDDDBCAAEooFFEGHIoEGHIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCDAABCDoEBoFGEooFGHHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCCCDBEEEDBoFGHooFGHAAoGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDDoBCEFGGoEFHHIEoooI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCCCDBoEEDFGHHDFGIIJJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCoooBoooEoAAFEGGGFE
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDoBECDooECDFFGGooooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBBBoCoDEoCFDEGCFDHGAAoHG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCoooBCoooBDoEEEDFFGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Cv1,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooBBBAAooCooooCoDEEEoDFFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBooCCBDooEFDoGEFooGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoooCCCoAADEFooDEFoooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDEoBCDEFoCooFoGGoHHII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBooAACDEoFCDEGFCoEGHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBEoCDoEFFoGoHHHGIIoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,I>1,Dv2,E<1,Cv1,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BooooBCDDDECFoGEoFHGoAAHG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBoECDBFECDoFoGGHHoII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDEoBCDEooFGoHHFGIIJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,C^1,G^1,I<1,J<1,Gv1,Cv1,A>2
</answer>


Board size: 5x5
Board: AABoCDDBoCEFGGHEFoIHEJJIo
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Hv1,G>1,Bv2,C>1,D^1,J<1,Fv1,F<1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCDEoBCDEooCDEoFFoooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoDDBCEFFFCEooGGooHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDooBCDEooFoEooFoGGHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooooBBBooCDDDoCAAEoFFoEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABooCCBDDEFGGHEFooHoFoII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,Hv1,G>1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABoCDoBECDFBEGHFooGHFIII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCoooBCDDDEoFFFEoGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDDoBCEoFBoEoFGGEoHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoooBCoooBCDEEEoDooFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBCCCDEAAFDEGGFHHIIoJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCCCoBAAoDBEEoDFGHHDFGIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBoAAoBCDEEECDFFFCGGHHo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Cv1,C^2,D<1,F<1,Cv2,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAABCoooBCoDEEEoDoFFoGGoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoDEBCFDEGCFoHGoooHII
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,Cv1,D^1,H^1,I<3,Gv1,Bv1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAAoBoCDDBECooBEFFGGEHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDEFBCDEFGoDoHGoooHII
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,Cv1,E^1,H^1,I<3,Gv1,Bv1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABooCoBoDCEEFDGGGFDoHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G>1,Cv2,E<1,Bv1,A>2
</answer>


Board size: 5x5
Board: BoAACBDDoCoEFoCoEFGGHHIII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDDBoCEoFFoEoGGGHHooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDoEBCDFEGGoFooHHFoooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,F>1,Bv3,E<2,Bv1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBCDAAoCDooEEDFoGGGFHHoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDEFBCDEFoGoHFoGoHIII
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>2,D^1,H^1,I<1,Hv1,Cv1,A>1
</answer>


Board size: 5x5
Board: BooCoBAACDBoEEDooFFooooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,D<1,F<1,Cv2,A>2
</answer>


Board size: 5x5
Board: oBBBCAAooCDEFFCDEGGGDHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDDoBCEoFFFEoGGGHHIIo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBCDDDECAAFECGoFHoGIIH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCooBoCoDDEEFFFoooGGHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDEBoCDEFFGHHoIGoooIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Gv1,F>1,Bv3,E<1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABoCDoBoCDoBoCoEFFooEooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABooooBoooCDDEECFFooGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCDBooEDBoFEDAAFEooooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooBAACoBooCDDooEEooFFFo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooooBoCDDEECooFFGoHHoG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E>1,F<2,H<1,Bv3,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCDooBCDooEEooFGGooFHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoooBCoDDoEoFooEoFoGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDEoBCDEoFFGooHHGIIIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I>1,Ev2,E<2,Bv1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABCDEEBCDFFooGoHHoGooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDDEBCoFEGHoFoGHooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDEoBCDEFBCooFGGoHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooBoAAoBCCDEEooDFFoooGG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDDoBCEFoGGEFoooEHHoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABooCDBooCDEEooFGGHHFoo
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,D^1,F^1,H>3,Dv2,Dv1,D<3,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAooBCCCoBDEEFFDGHIJoGHIJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCDoBoCDooEFFFoEoGHoAAGH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BAACoBooCoDEoCoDEFGGooFHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABoCCCBDEFGGDEFooooHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBoCCoBDEEFFDGGGooHHII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooooAAoBooCCBDDEoBFFEGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCoBooDEAAoDEoFGHIIFGH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCCDoBooDoEFoDoEFGGHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCoDBoCEDFFoEDoGGHHoII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Bv3,E<1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCDDoBCEoFFFEoGHHIIGJJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBoCDEEECDFGGGoFooHAAooH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBCAADECFFDEGHHoEGIIJJ
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBooooAAoDoEEoDoFFFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBooAABCoDDBCooEEoFooGGF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,E<1,G<2,Bv2,A>3
</answer>


Board size: 5x5
Board: oAAoBoCooBDCEEEDFoGGDFooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDDDBCEFoGGEFoHHEIIoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I>1,Fv1,F<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCDEoBCDEoFFooooGHoooGH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoooBCoDoBoEDoFFEGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBAACoBooCDEFFFDEGGoHHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCoAAoCDEEFFDGGHHIIoJJ
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDoBCoDoBoEDFFoEoGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBDEFGHDEFGHDoIJAAoIJ
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>1,Hv1,Bv1,B<2,F^1,G^1,I^1,J^1,A>2
</answer>


Board size: 5x5
Board: BooooBCDDDoCEEEFoAAGFoHHG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCAADBCEoDBoEFoooEFGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv2,Cv1,F^1,G<1,Bv2,A>3
</answer>


Board size: 5x5
Board: AABoCooBoCDEEooDoFGGooFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Dv1,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: oBBBoCDAAECDooEFDGGGFoHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAABCoooBCooooCoDEEEoDoFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBooCDBooEFoGGEFoHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABoCoDBECoDFEGHoFEGHIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCooBoCDDDoEEEoooFFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooBoAAoBCoooBCDDEECoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoDDBCooEBCFoEGGFoHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABooCCBooDEEooDooooFFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCCCDBooEDoooEDAAFEoGGFHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oooooBCCCoBooDEAAoDEFFGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBoECDFGEoDFGHHHIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBCDAAoCDooooDEEFFoGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCoBDooEBDoFEAAoFGGHHF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCooBoCoDEEoFDoooFooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Dv1,D<2,Bv1,A>3
</answer>


Board size: 5x5
Board: oBAACoBoDCEFFDGEHHHGEIIJJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,I<1,J<1,Gv1,Cv1,A>1
</answer>


Board size: 5x5
Board: AABoooCBDooCEDoFGEoHFGIIH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^1,I>1,Ev1,Bv1,A>3
</answer>


Board size: 5x5
Board: oBBBoAACDEFGCDEFGooEooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAooBooCoBDDCEEFFoGGooHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C^1,E<1,G<1,H<1,Cv3,D>1,Bv1,A>3
</answer>


Board size: 5x5
Board: oBBBoAAoCDEFFCDEGGGDoooHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCoDBoCEDFFoEGGooEoHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBoCCoBDoEFFDoEGGoHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooCCBDDEEFooGoFHIGJJHI
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H^1,I^1,J>2,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooAABoooCBDDoCBEFFGGEHHoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCoAABCDEEECDFFFoooooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCoDBoCEDFFCEoGGooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oooooAABCDoEBCDFEBoDFoGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACoBDoCEBDFFEoGGoEHHooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,H>2,Dv2,E<1,Cv1,A>2
</answer>


Board size: 5x5
Board: BAACDBEoCDoEooFoGGGFooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABCoDoBCEDFFCEoGGoEHHH
Optimal length (moves): 10
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<2,D^1,E^1,F<1,G<1,H<1,Cv3,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: BAACDBooCDBEEoDoFFGGooHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoooBCooDEoFoDEoFoDGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,G>1,Ev1,Bv1,A>3
</answer>


Board size: 5x5
Board: oBBBCoAAoCDoEECDoFFFDGGHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBDoEoBDFEoAAFEGoHHHG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoBCDDDBCoEoFFGEoooGHHoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>1,Ev1,E<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oooBCDAABCDoEECoFFFoooGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCoAAoCDoEFFDGEoooGoHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABooCDBooCDBoEoDFFEooGG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCDooBCDEEECoFGGHHFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBoAAoBCooDDCoEEECoFFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,C<1,E<1,Bv2,A>3
</answer>


Board size: 5x5
Board: ooooBAAooBoooooCDEEECDoFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCoDDBCEFFFoEooGGHHooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAooBCoDDBCEEFFoGGooHHHII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCAADBCEEDFGooHFGooHoIIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCDBooEDoooEFFFoGooAAG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCCCBoDooEFDGHEFDGHII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBooooBCDEFFCDEoGGoHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooBCAADBCooDBEooFFEoGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCoDDBCEoooCEFFGGHHHoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBoAAoBoCDDBECoFFECGGGE
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: ooBCDAABCDooEEDFooooFoGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDDBoCEFFoCEooGGoHHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCoDDBCEEooCooFGGHHFII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABoCCoBDoEFFDoEoGGoHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCoooBCDEEECDoooFFGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCoDoBCoDEEoFFGGoHHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDooBCDEEoFDoooFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Cv1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAoBooCoBooCDDoooEEEoFFFo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBooAAoCDEFFCDEGGCDEoHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoDDBCoEFFoGEHooGoHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Ev1,E<1,Bv1,A>2
</answer>


Board size: 5x5
Board: BoooCBoooCooAADoEFoDoEFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<2,F^3,G<1,Ev1,A>3
</answer>


Board size: 5x5
Board: AAoBCoDoBCEDooFEGGGFoooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCDooBCDEEECFooGoFooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDoBoCDEEFGoHoFGoHIIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<1,Bv1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: BAAoCBDDDCEFFGGEHIJJoHIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BooCDBAACDEoFFDEoGGoEoHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BCDDDBCooEFAAoEFoGHHFoGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDDBCEFoGGEFoooEHHIIo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I>1,H>1,Fv1,F<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCDooBCDoooEEFGGoHFIIoH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCooooooEFGAAEFGHHHF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBDooEBDoFEooGFHAAGFH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCoAADCEEoDCooooooFFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,F<1,G<1,Cv2,A>2
</answer>


Board size: 5x5
Board: AAoBCDDoBCEFFFGEoooGooHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,Bv1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABoCCoBoooDEEooDoooFFFo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oooBooAABoCoDDDCEEEFooooF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCDooBCDooBCEEFFGGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBooCCBDEEFFDooooooGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBCCCoBoooDAAEFDoGEFooGHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooooBoooCBDDDCooEooAAEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDooCBDEoFoGEoFoGHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,G^1,H<1,Gv1,Dv1,A>1
</answer>


Board size: 5x5
Board: AAoBoCoDBoCoDEEoFooooFGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCDDBoCoEEEooFFoGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBooCooooCDDDEoAAFEGGoFo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBooAACDEEoCDFFGGDHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoooBCDEoFFDEGGoDoHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: BBBCDEAACDEooFFoooGGHHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDooCBDEFFooEooooGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCDEoBCDEFFCDGGoHHIIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,F<1,Cv3,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: oooooooAABooCoBooCDDooEEE
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BooCDBAACDooEEEoooFFGGHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBoCDAAoCDooEEDFFGGHHoII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBCDAABCDoooCoooEEooFFFo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,E<2,Bv2,F<1,Bv2,A>3
</answer>


Board size: 5x5
Board: ooooBooAABoCCoBDEEFFDGGHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCooDBCoEDBCoEDFFooGGo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDooBCDEFFGDEHHGooooII
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Ev1,E<1,Bv1,I<2,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooAABCDEoBCDEFFCGGoHoIIoH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCooDBCooDBEFFDoEoooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCDooBCDEEECFFoGoHHoG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BCCCoBooDoAAoDooEEFFGGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAACDBooCDEEFFGGGooHHIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCooAACoDDoCEooooEFFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCoAADCEFFDCEGGGooHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDooBCDoEEFDGGHFoooHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCDEAACDEooCDFFGGoooHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDooBCDoEEEoooFFGGHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBooCDBAACDBEECFFoGGoHHII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: ooAABooCCBDDEoBFFEGGoHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDoEBCDoEBoDFoGGoFoHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BooooBCDDDECooFEAAoFoGGGF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDooBCDooBEooFFEGoHHoG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Ev1,Cv1,E<1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAAoBooCoBoDCEFoDCEFoGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBCDEoFCDEGFoDEGHAAoGH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBCoAABCDEEooDoooFFGGoHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAAoCBDDoCoEEoCFGHHHFGoII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BAACDBEFCDGEFHoGooHoGooII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,I<2,Hv1,Cv1,A>2
</answer>


Board size: 5x5
Board: AABoCDDBoCEFFGHEooGHooIIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,Bv1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooBBBoCDoEoCDFEooDFGoAAFG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDDBCoEoBoFEGGoFHHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBCoAAoCoDDoCoEFFFoEGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooBoAAoBCoDDDCEEFFooGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBooCDEoFFFEGGGooHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDoBCEDFFoEoGoHHoGIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv2,E<1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABoCDoBECDFGEHDFGoHoIIoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Hv1,Cv1,I<1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooAABCCDoBEoDFFEGHHooGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>1,Dv2,E<1,Bv1,A>1
</answer>


Board size: 5x5
Board: oAABCoDoBCoDooCEoFGGEoFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCDEEBCDFFFGGHIoJJHIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCooBoCoDDEEoFFFoGGGoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBooooBCooDECFoDECFGGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,G<1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCDDDBCEoFFFEGGGoHHIIo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCAAooCDDDooEFFGGEHHII
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoBCDEoBCDEFoGDEFoGHHoII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCooBDCEEBDCFFFDooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCAAooCDEFFFDEoooGGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>2,Ev1,E<1,Cv2,A>3
</answer>


Board size: 5x5
Board: AAooBooCCBoDEFFoDEooGGGoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,E^2,F<1,Cv3,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooAABooooBCDDEECooFFoooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABCDDDBCEEFFoooGGHHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBoAAoCDEooCDEoFFDoGGHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCoooBCDEoBFDEGGFHHIIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E^1,Fv1,Cv1,F<1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BBBooCoDDDCooEFoAAEFoooEo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACoBDoCEBDFFEGHHoEGoIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H>1,Dv2,E<1,Cv1,A>2
</answer>


Board size: 5x5
Board: oAABCDDoBCEoFoCEoFGGoooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABooooBoCDEEoCDFGGGDFooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
E>1,F^2,G<1,Dv2,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: BAACDBooCDoEEFoGooFoGoHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,G^1,H<2,Gv1,Cv1,A>2
</answer>


Board size: 5x5
Board: oBBBoAAoCoDEECoDoFFFDGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBAACoBDoCoBDEEFFoGooHHGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
H<1,Dv2,D<1,Cv1,A>1
</answer>


Board size: 5x5
Board: BAACDBoECDoFEGHIFoGHIFJJo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F^1,Hv1,Dv1,J<1,Gv1,Cv1,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BoAACBDooCBDEFFoDEooGGGoo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A<2,E^2,F<1,Cv3,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABooCoBoDCoEEDCooFFooGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,G<1,Dv2,D>1,Bv1,A>3
</answer>


Board size: 5x5
Board: BooooBAACDBEECDoFFFDoGGHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDDoBCEoFGoEoFGoooHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,H<1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAoBooCCBDoEFFDGEHHHGIIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABooCDBoECDFGEHDFGEHII
Optimal length (moves): 11
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDEoBCDEoBCFoGHHFoGIIo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,Dv1,F^2,G<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCDDDBCoEFFooEoooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,Ev1,E<1,Bv1,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oBBBooCAADoCEEDoCFFFGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCooBoCoDDDooEooFFEGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBoDDCooooCooEFFooEoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBCDEEECDoAAFGHHoFGIIJJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBoCCDBEFFDBEGGHHooIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBooCCBDDEFFGGEooooHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<2,E^2,F<1,H<1,Cv3,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: BAACoBDDCEBoFCEooFGGoooHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCoDDBCEEFFGGGooooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoBCDDoBCEEEoFGHooFGHoII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAooBCCooBDEFoGDEFoGHHFII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCDAABCDoEECFooooFooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oooBCAAoBCDDoooEoFFFEGGHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBEECDFGoHIFGoHIooJJo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Iv1,Dv1,J<1,Hv1,Cv1,A>2
</answer>


Board size: 5x5
Board: BCCCDBEEEDoooFoAAoFoGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCooDBCooDoEEoFFFoooooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F>1,Dv2,D<3,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: ooAABCoDDBCEEFFGGoHHoIIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BAAoCBDDECoFoECoFGHHoFGII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv2,C<1,G^2,H<1,Bv1,A>2
</answer>


Board size: 5x5
Board: oAABCoooBCDEEBCDFFFoDGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDDDBCoEEFoGooFoGoHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCDoAACDoEEEDooFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBBBCooDECFGDECFGDHAAGoH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDooBCDEEoFoGGHFIJJHoI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Cv1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAoBCDEEBCDoFFGDooHGIIoHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,Bv1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAAoBCooDBCEEDBCFFGGooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAAoBoCooBDCEEEDFFFoooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oBBBCoDAACoDEEooDFFFooooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,B>1,C^1,F<1,Dv1,A>1
</answer>


Board size: 5x5
Board: oBBBCAAooCDoEoCDFEoooFEGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCDAAoCDooEEDoFFFooGGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv2,D<1,F<1,Cv2,A>3
</answer>


Board size: 5x5
Board: AAooBCoDDBCEEoBCFFGGoHHoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBEECDBooFGHHoFGIIIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooBCoAABCoDDoCEoFFoEooGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBooCAAoDCEFFDoEooDoEGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAAoBooooBCDDEECFFGGHHIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBCoDDBCEEFFGGHHHIIIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoooBCooDoCooDoEEFFFoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACoBDoCEoDFFEGGoooooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>2,Dv2,E<1,Cv1,A>2
</answer>


Board size: 5x5
Board: BCDDDBCEFoooEFGAAoFGooooG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCCoBooDDBoEFFFGEoooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoCCCBDDDEBAAFEoGoFooGHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABooCCBoooDEoFFDEoooDGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
C<1,D^1,G<2,Ev1,Bv1,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoBoCDDBECFFFEGGHIJooHIJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCAADBCEEDBFGGGoFoHHoIIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I>1,Fv1,F<1,Dv1,A>1
</answer>


Board size: 5x5
Board: oAABCoDDBCoEEBFooGGFoHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBoCDoBoCDoBECFFFEGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: AABoCDDBoCEEoFFGGoHooIIHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAAoBooCoBDDCEEFGGooFoHHH
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBooCDBEECFoGGGFooooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,Dv1,F<1,Cv1,A>2
</answer>


Board size: 5x5
Board: AAoBooCoBooCDDoEFFFGEHHHG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G^2,G>1,H>1,Cv2,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: AAoBoCooBDCEEEDFooooFoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABCoDDBCoooECoFoEooFGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,G>2,Ev1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCoDDBCEFFoGEHHoGoooII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCDDEBCFFEGCoHHGooIIIo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,I<1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: BCCCDBooEDoAAEFGGoHFIIIHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDoBCoDEEooFFooooooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BooCDBAACDEEooDFoGGoFooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBooCDEEFCoooFGGoHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABoCCCBDoEEBDFFGGDoooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABCDEEBCDoFBGoHFoGIHFooI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,Cv1,Gv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oBAACDBEoCDBEFFGoHHoGoIII
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A<2,E^1,F<1,I<1,Cv3,E>1,Bv1,A>3
</answer>


Board size: 5x5
Board: BAACDBooCDoEFGDoEFGoooFHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,F^1,H<2,Gv1,Cv1,A>2
</answer>


Board size: 5x5
Board: ooBCDAABCDEEoCooooFFooGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBooooBCoDoECFDoEoFDoGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooAABCCDDBEEFFGoHHHGoIIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBCoAADCEooDCEooFFooGGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,F<2,Dv1,G<1,Cv2,A>3
</answer>


Board size: 5x5
Board: AAooBCDDDBCEEFFGHHooGoIII
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: oAABCoDEBCoDEoCoDFFFoGGoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BoAACBDDECFooEGFoHHGoIIJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
I<1,J<1,Gv1,Cv1,A>1
</answer>


Board size: 5x5
Board: oAABCDDEBCoFEGGHFIIoHoJJo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,E^1,Fv1,F<3,Bv1,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oooooBCDDDBCooEAAooEoooFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCDDDBCoEoFGoEoFGoHHoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: ooooBCAAoBCDEEooDFFFGGGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDDBCEFGGCEFoooHIIooH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,I>1,Fv1,F<1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABCooDBCEEDFGoHHFGIIooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.


Board size: 5x5
Board: oAAoBoCCDBEooDFEGHDFoGHII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: BAACDBooCDooECDFoEGGFHHHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BCDDDBCEFoBCEFGAAooGooHHG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BAACDBoECDFGECDFGoHHIIJJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AAoBCooDBCoEDFCoEDFooooGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,G<2,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAABooCDBooCDEEoFFooooGGG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A<1,D^1,F>1,Dv2,D<3,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: BCDDDBCEFooCEFooooGooAAGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: oAABCoDoBCEDoFFEooooEGGoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Dv2,E<2,Bv1,Bv1,A>2
</answer>


Board size: 5x5
Board: oooBooAABoCoDEECFDoooFGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Dv1,D<2,Bv2,A>2
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AABCDooBCDoooCoEFGGGEFooo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCooBoCDDEEFooGGFooHHo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Fv1,E>1,F<2,H<2,Bv3,D<1,Bv1,A>3
</answer>


Board size: 5x5
Board: oAAoBooCoBDoCoBDEEFFDGGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCDooBCDoEECooooFFooGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,E<1,Bv1,F<2,Bv1,A>3
</answer>


Board size: 5x5
Board: BAACDBEECDBFooGoFooGoooHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,H<1,Gv1,Cv1,A>2
</answer>


Board size: 5x5
Board: BAACDBooCDooooEooooEoooFF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABoCDDBoCEFFoGEoooGoooHH
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,Bv1,H<1,Fv1,Bv1,A>3
</answer>


Board size: 5x5
Board: AABCoDoBCoDoEoFooEGFoHHGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv1,H<1,Ev1,Bv1,A>3
</answer>


You are an expert Rush Hour (5×5) solver.

Input: 25-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: 5x5
Board: AAoBCDDEBCFGEHHFGoIJFooIJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev2,Fv1,F<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: BooCDBAACDBEoCDoEFooooFGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: AABCoDoBCEDoFFEGGGoEoHHHo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
G>1,Dv2,E<2,Bv1,Bv1,A>3
</answer>


Board size: 5x5
Board: BCDDDBCEFooCEFGAAooGHHooG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
A>2,Cv1,C<1,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: oooooBCoAAoBCoDooBooDoooooDooooooEEE
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAoBoooCCBoDoooBoDoooooDEEoFFoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBCDoooBCDoEAAoooEFoGHIJFKGHIJFKGHIJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AAooBoooooBooooooooooooooooCoooooCDD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooooooooooooooAAoBoooooBoooCCBo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooBoooAABooCCooooDDooooooEEEooooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oBoooooBooooooooooooCoooAACoooooCooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooAAoBooooCBDDEoCoFoEGHHFIoGooFIoGJJ
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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

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


Board size: 6x6
Board: ooooooAABoooooBCooooBCoDoooCoDEEoooD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooBBBooooooCoAAooCDDEFGGHoEFooHooFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBCCCDoBoooDoBEEEDFAAoGoFHHIGoFooIo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: AABoooooBoooCoBoooCooDDDCoEEEooFFFoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooBCooooBCooooBoooooDEooooDEooAAoEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oAAooBoCCCDBooooDooooooooEEEFoooooFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooAAoBoooooBoooooooooooooooCCC
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: BooCCCBoooooBoDoooooDoEoAAooEoooooFF
Optimal length (moves): 2
Return only the <think> and <answer> blocks.


Board size: 6x6
Board: ooBCoDooBCoDAAoooDoEooFooEGGFooEHHFo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv3,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: oooBoooAABoooooBooCoooooCDooooCDoooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooooooooooooooBCoDAABCoDooBoooooo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooooBCooooBCoAAoBCoooDoooooDoooEEoo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: ooooooooBBBooCoooooCoooDoooooDoooAAD
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: oooAABCCCooBoooooBoooooooDDoEoooooEo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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


Board size: 6x6
Board: BCoDDDBCoooEoCoooEFGGGoEFoAAHoFoIIHo
Optimal length (moves): 2
Return only the <think> and <answer> blocks.

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