
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 each value of $x_1, x_2, x_3, \ldots, x_n$ can only be one of -2, 0, 1, and satisfies $x_1 + x_2 + \ldots + x_n = -17$ and $x_1^2 + x_2^2 + \ldots + x_n^2 = 37$, find the value of $x_1^3 + x_2^3 + \ldots + x_n^3$.

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