
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In how many ways can a rook move from the bottom left corner square (a1) to the top right corner square (h8) on a chessboard, approaching the target with each step: a) in 14 moves, b) in 12 moves, c) in 5 moves?

Present the answer in LaTex format: \boxed{Your answer}
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