
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
Complex numbers \( z \) satisfy both \( z^{26} - z^{10} - 1 = 0 \) and \( |z| = 1 \). Express these numbers as \( z_m = \cos\theta_m + i\sin\theta_m \), where \( 0 \leq \theta_1 < \theta_2 < \dots < \theta_{2n} < 360^\circ \), with angles in degrees. Calculate the sum \( \theta_2 + \theta_4 + \dots + \theta_{2n} \).

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