
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
There is an unpainted board of size $101 \times 201$. The first player has a bucket of yellow paint, and the second player has a bucket of blue paint. Each player, on their turn, can paint an entire row or column with their color. When yellow and blue paints are mixed, green is produced. Further mixing of green with either yellow or blue does not change the color. A player cannot paint a row or column if it has already been painted by the opponent, nor can they paint if it does not change any cell's color on the board. The player who cannot make a move loses. Who can guarantee a win?

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