
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
Let the real numbers \( x_{1}, x_{2}, \cdots, x_{1997} \) satisfy the following two conditions:
1. \( -\frac{1}{\sqrt{3}} \leq x_{i} \leq \sqrt{3} \) for \( i = 1, 2, \cdots, 1997 \);
2. \( x_{1} + x_{2} + \cdots + x_{1997} = -318 \sqrt{3} \).

Find the maximum value of \( x_{1}^{12} + x_{2}^{12} + \cdots + x_{1997}^{12} \) and justify your answer.

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