
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 with dimensions \( m \times n \), there is a rook. Two players take turns moving it vertically or horizontally by any number of squares; at the same time, it is not allowed for the rook to land on or pass through a square it has already visited (or through which it has already passed). The player who cannot make a move loses. Who among the players can guarantee a victory: the one who starts or the partner, and how should they play?

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