
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
If $\phi$ is a constant such that $0 < \phi < \pi$ and $x + \frac{1}{x} = 2\sin{\phi}$, then for each positive integer $n$, $x^n + \frac{1}{x^n}$ equals:
A) $2\sin\phi$
B) $2^n\sin\phi$
C) $2\sin^n\phi$
D) $2\sin n\phi$
E) $2^n\sin^n\phi$

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