
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 \( 2 \cos \vartheta = u + \frac{1}{u} \), then simultaneously \( 2 \cos n \vartheta = u^n + \frac{1}{u^n} \) for any integer \( n \).

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