
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. \(-\frac{1}{\sqrt{3}} \leqslant x_{i} \leqslant \sqrt{3}\) 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 give a reason for your answer.

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