
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 the corner of a chessboard of size \( m \times n \) squares, there is a rook. Two players take turns moving it either vertically or horizontally by any number of squares; it is not allowed for the rook to land on or pass through a square it has already visited (or passed through). The player who cannot make a move loses. Which of the players can ensure their victory: the starting player or their partner, and how should they play?

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