
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
Game with dominoes. Given a $10 \times 10$ grid. In each turn, it is allowed to cover any two adjacent cells with a domino (a $1 \times 2$ rectangle) such that the dominoes do not overlap. The player who cannot make a move loses.

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