
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
There are $4n$ complex numbers that satisfy both $z^{36} - z^{12} - 1 = 0$ and $|z| = 1$. These numbers have the form $z_{k} = \cos\phi_{k} + i\sin\phi_{k}$, where $0\leq\phi_{1} < \phi_{2} < \dots < \phi_{4n} < 360$ degrees. Find the sum of $\phi_{2} + \phi_{4} + \dots + \phi_{4n}$.

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