
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
Find the sum of angles, in degrees, of the solutions to the equation \(z^6 = -32\), where each solution \(z_k\) can be expressed in the form:
\[
z_k = r_k (\cos \theta_k + i \sin \theta_k)
\]
for \(k=1, 2, \dots, 6\), where \(r_k > 0\) and \(0^\circ \leq \theta_k < 360^\circ\).

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