
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
For a chessboard with $m$ columns and $n$ rows, if the first player's piece is on the upper left corner and the second player's piece is on the lower right corner, determine the pairs of $(m,n)$ for which the second player has a strategy that guarantees a win.

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