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

<think>
Shortest path found.
</think>
<answer>
C^1,G^1,I<1,J<1,Dv1,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: oooBCoooBCAAoDEFooDEFGGGo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Fv1,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: oAABooooBCDEoFCDEoFCDoGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Ev1,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: AABCDEEBCDFoGHoFIGHoFIooo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Dv1,Gv1,Bv1,Gv1,Bv1,A>3
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,H<2,Gv1,Bv1,A>3
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Ev1,E<2,Bv1,Bv1,A>3
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F<2,Dv1,D<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: AAoBCoDoBCoDooCEFGHHEFGoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev2,Ev1,E<2,Cv1,Cv1,A>2
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
G>2,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: oAAoBooCoBDoCEEDFFooDoGGG
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,H<1,Cv2,A>3
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<2,Bv1,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: oAAoBCDooBCDEEECFFFoooGGo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv1,J<1,Hv1,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: oooBoAAoBoCDDBECoFFECoGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


Board size: 5x5
Board: AABooCCBDoEFFDoEooGGHHooo
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>


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: oBBBoCDDDECooFEoooFGoAAFG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,G>2,Cv2,Dv1,D<2,Bv1,A>3
</answer>


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
G^1,I<1,Gv1,Bv1,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: BAACDBEECDooFFDGooHHGIIoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


Board size: 5x5
Board: ooooBoCCCBAADEoFoDEGFHHoG
Optimal length (moves): 12
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
D^1,E>2,F^1,G^1,H<3,Fv1,F<1,Cv3,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: AAooBoooCBDDECFGoEoFGoEHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,G^1,A>1,Bv1,B<2,F^1,G^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: AABCoDoBCoDoBooDoEEFooGGF
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


Board size: 5x5
Board: BBBoCooAACoooDDEFFGGEoHHH
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,Cv2,A>1
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,H<2,Gv1,Bv1,A>3
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F<1,Cv2,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: AAooBoCDoBECDFFEGGooHHoII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,E^1,G<2,Fv1,Bv1,A>3
</answer>


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
A<1,D^2,E<3,Bv1,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: oAABoCCDBoooDEEFGHoIFGHoI
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


Board size: 5x5
Board: AABoCoDBoCEDooFEGGoFEoHHH
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>


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: AAoBooCDBoECDFFEGGooHHHoo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,G>1,H>2,Dv2,Dv1,D<3,Bv1,Bv1,A>3
</answer>


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

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


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

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


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

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


Board size: 5x5
Board: AAoBoCDDBoCEEEoFFFGGHHIII
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>


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

<think>
Shortest path found.
</think>
<answer>
I^1,J<1,Hv1,Cv1,A>1
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
I^1,J<2,Iv1,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: AAooBooCoBooCDDooEooFFEoo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Cv2,Dv1,D<2,Bv1,A>3
</answer>


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
D<1,G^1,H<1,Fv1,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: BAACDBEFCDGEFoDGEHHHGIIIo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


Board size: 5x5
Board: BAACoBoDCoEFDGGEFHHIoJJoI
Optimal length (moves): 15
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Ev1,Bv1,A<1,D^1,F<1,I^3,G>1,I>1,J>2,Bv3,Ev1,E<2,Bv1,Bv1,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
C^1,Dv2,D<2,Cv1,A>2
</answer>


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

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


Board size: 5x5
Board: AABoCDoBECDFFEoDGGHooIIHo
Optimal length (moves): 12
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Cv3,D^1,E>2,Bv1,A>1,C^1,F<1,I<1,Dv2,D<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: ooAABCCCoBoDEFGHDEFGHIIJJ
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E^1,F<3,Bv1,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: AABoCDDBoCoEEFFGGoHHIIoJJ
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Ev1,E<1,F<1,Dv1,A>1
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv1,Cv1,H<2,Gv1,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: AAoBooCDBooCDEEoFFoooGGGo
Optimal length (moves): 8
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E<1,G^1,H<2,Cv2,Cv1,A>2
</answer>


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


Board size: 5x5
Board: BooooBAAoCBoDDCoEFFFoEGGo
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>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,E^1,I<1,Gv1,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: AABooCDBEoCDFEGoHFEGoHIIG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
A>1,D^2,E<1,F<1,G<1,H<1,Dv2,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: AABoCoDBECFDBEoFGGHooooHo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
A>1,Dv1,D<1,F^1,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: AAooBCDDoBCEFFFCEoGHIIIGH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
H>1,Dv1,Bv1,A<2,E^2,F<1,Cv3,E>1,Bv1,A>3
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,D^1,G^1,H<3,Fv1,Bv1,Fv1,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: AAoBCDDDBCoEoFFoEGGooHHHo
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: oooooBCCCoBooDEAAoDEoooDE
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F^1,G<1,H<1,Cv2,E>1,Bv2,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: AAoBCoDDBCEFFFGEoHHGoIIIo
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: BBBoCAAooCDDEECoFFGGooHHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Dv1,F^1,G<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: AABCoDEBCoDEoFFooGGHIIIoH
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
F<1,H^1,I>2,Dv2,Dv2,D<2,Bv1,Bv1,A>3
</answer>


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
H<1,I<1,Fv1,Bv1,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: ooooBoAACBDoECoDFECoDFoGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


Board size: 5x5
Board: AABCoooBCooDEEooDooFoGGoF
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>3
</answer>


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

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


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

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


Board size: 5x5
Board: BAACDBooCDEFooDEFGGGEoHHo
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>


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: AABooCCBooDEFFGDEHHGIIooG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


Board size: 5x5
Board: oBBBoooooooCDDDoCoEoAAoEo
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>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv1,E^1,G<1,Fv1,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: BoCCCBAADoooEDFGHEDFGHIII
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv1,F<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: AABCoooBCooDBCEoDFFEooGGG
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
C>1,F^2,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: AAoBCDDDBCEoFFGEoooGEooHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


Board size: 5x5
Board: AABoCooBDCEFFDoEGGHHEIIoo
Optimal length (moves): 12
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
D^1,F>2,Bv1,A>1,E^2,G<1,I<1,Ev2,E<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: BBBoCAAooCDEEEoDFFGGooHHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
I>2,Ev2,Ev1,E<2,Bv1,Bv1,A>3
</answer>


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

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


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

<think>
Shortest path found.
</think>
<answer>
G^1,I>1,H>1,Bv2,B<2,C<2,E^2,F^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: AABCDooBCDoEoCooEFFoGGoHH
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
G<1,Ev2,E<2,Bv1,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: oAABCooDBCEEDBCooDFFooGGG
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,Bv1,Gv1,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: AABoCDEBoCDEoFFDGGHHoIIoo
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

<think>
Shortest path found.
</think>
<answer>
Bv1,A>1,C^1,G<1,I<1,Ev2,E<1,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,G^1,I<2,Gv1,Bv1,A>3
</answer>


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
E^1,H^1,I<2,Gv1,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: AABCDEEBCDooooFooooFooGGG
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv2,B^1,F^1,H<2,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
Cv1,C<1,F^1,H^1,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: AABCDooBCDoooCEFGGGEFHHII
Optimal length (moves): 9
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
F<2,Dv2,A>2,Bv1,B<1,D^1,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: AAoBoCooBoCDEBooDEFFGGooo
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

<think>
Shortest path found.
</think>
<answer>
Cv1,Dv2,E<1,Bv1,A>3
</answer>


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

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


Board size: 5x5
Board: oAABCoooBCDDoBEoFGoEoFGHH
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>2
</answer>


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
C^1,E^1,F<1,Dv1,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: AAoBCoDEBCFDEGoFHHGIoJJJI
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Bv1,A<1,D^1,E<2,F<2,Cv3,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: BBBoCAAooCooooCDEEFFDGGoo
Optimal length (moves): 6
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv2,Dv1,D<2,Cv1,A>2
</answer>


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

<think>
Shortest path found.
</think>
<answer>
E<1,Cv2,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: BCCCDBooEDAAoEoFFFoooGGHH
Optimal length (moves): 5
Return only the <think> and <answer> blocks.

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Gv1,I<1,Ev2,A>1,Bv1,B<1,E^1,A>2
</answer>


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

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


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

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


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

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


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

<think>
Shortest path found.
</think>
<answer>
Dv1,D<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: AAooBoCooBoCDDBEEFGGooFoo
Optimal length (moves): 7
Return only the <think> and <answer> blocks.

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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


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

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


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

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