
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
Consider an \( n \times n \) chessboard. It is necessary to move a rook from the bottom left corner to the top right corner. The rook can move only up and to the right, without landing on the cells of the main diagonal or below it. (The rook is on the main diagonal only at the start and end moments.) How many such routes exist for the rook?

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