
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
Given \( n \) numbers \( x_{1}, x_{2}, \cdots, x_{n} \), each of which is one of \( 0, 1, -1 \). If \( x_{1}+x_{2}+\cdots+x_{n}=1000 \), calculate the value of \( x_{1}^{2017}+x_{2}^{2017}+\cdots+x_{n}^{2017} \).

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