
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 \( x_{1}, x_{2}, \ldots, x_{n} \) be a sequence in which each term is 0, 1, or -2. If

\[ \begin{cases} x_{1} + x_{2} + \cdots + x_{n} = -5 \\ x_{1}^{2} + x_{2}^{2} + \cdots + x_{n}^{2} = 19 \end{cases} \]

determine \( x_{1}^{5} + x_{2}^{5} + \cdots + x_{n}^{5} \).

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