
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 \(2n\) complex numbers satisfying \(z^{28} - z^8 - 1 = 0\). They have the form \(z_{m} = \cos \theta_{m} + i \sin \theta_{m}\), \(m = 1, 2, \cdots, 2n\), where \(0 \leqslant \theta_{1} < \theta_{2} < \cdots < \theta_{2n} < 2\pi\). Find the value of \(\theta_{1} + \theta_{2} + \cdots + \theta_{2n}\).

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