
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
For which $n$ can values of the variables $x_{1}, x_{2}, \ldots, x_{n}$ be chosen from the set $\{+1, -1\}$ such that the equation $x_{1}x_{2} + x_{2}x_{3} + x_{3}x_{4} + \ldots + x_{n-1}x_{n} + x_{n}x_{1}=0$ is satisfied?

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