
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
Determine all complex numbers $z$ such that $z^{24} - z^{16} - 1 = 0$ and $|z| = 1$. These numbers are expressed in the form $z_{m} = \cos\theta_{m} + i\sin\theta_{m}$, where $0\leq\theta_{1} < \theta_{2} < \dots < \theta_{2n} < 360$. Calculate $\theta_{2} + \theta_{4} + \dots + \theta_{2n}$.

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