
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 all solutions to $z^5 = -32$, express them in the form $z = r (\cos \theta + i \sin \theta)$ where $r > 0$ and $0^\circ \leq \theta < 360^\circ$, and compute $\theta_1 + \theta_2 + \theta_3 + \theta_4 + \theta_5$, where $z_1, z_2, z_3, z_4, z_5$ are the solutions.

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