
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
Two persons are playing the following game on a  $n\times m$  table, with drawn lines:
Person  $\#1$  starts the game. Each person in their move, folds the table on one of its lines. The one that could not fold the table on their turn loses the game.
Who has a winning strategy?

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