
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
On a board, the numbers $1^{2}, 2^{2}, 3^{2}, \ldots, 1000^{2}$ are written. Two players take turns erasing one number from the board until only two numbers remain. If the difference between these two numbers is divisible by 13, the second player wins; otherwise, the first player wins. How should the second player play to ensure victory regardless of the opponent's moves?

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