
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 $2n$ complex numbers that satisfy $z^{36} - z^{12} - z^3 - 1 = 0$ and $|z| = 1$. These numbers can be represented in the form $z_{k} = \cos\theta_k + i\sin\theta_k$, where $0\le \theta_1 < \theta_2 < \dots < \theta_{2n} < 360$ degrees. Find the sum $\theta_1 + \theta_3 + \dots + \theta_{2n-1}$.

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