
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 players are playing on a $3 \times 100$ board: they take turns placing $1 \times 2$ dominoes on free cells. The first player places dominoes lengthwise along the board, and the second player places them crosswise. The player who cannot make a move loses. Which player can ensure a win (no matter how their opponent plays), and how should they play?

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