
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 take turns placing non-overlapping dominoes on a $2021 \times 2021$ board, each covering two squares. The second player’s goal is to cover the entire board with dominos except for one square, while the first player aims to prevent the second player from achieving this. Who can guarantee a win?

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