
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 there be $n$ numbers $x_1$, $x_2$, …, $x_n$, each of which can only take one of the three values 0, 1, or -2, and $x_1+x_2+…+x_n=-5$, $x_1^2+x_2^2+…+x_n^2=19$. Then, find the value of $x_1^5+x_2^5+…+x_n^5$.

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