
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 the sum of the angles of the solutions to the equation $z^6 = 64i$ in degrees, where the solutions can be expressed as $z_k = r_k (\cos \theta_k + i \sin \theta_k)$, with $r_k > 0$ and $0^\circ \le \theta_k < 360^\circ$ for $k=1, 2, ..., 6$.

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