
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 that the values of \( x_{1}, x_{2}, \cdots, x_{n} \) can only be \(-2\), \(0\), or \(1\), and they satisfy the following conditions:
\[
\begin{aligned}
& x_{1} + x_{2} + \cdots + x_{n} = -17, \\
& x_{1}^{2} + x_{2}^{2} + \cdots + x_{n}^{2} = 37,
\end{aligned}
\]
find the value of \(\left(x_{1}^{3} + x_{2}^{3} + \cdots + x_{n}^{3}\right)^{2}\).

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