
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
The solutions to the equation $z^5 = -32i$ can be expressed in the form
\begin{align*}
z_1 &= s_1 (\cos \alpha_1 + i \sin \alpha_1), \\
z_2 &= s_2 (\cos \alpha_2 + i \sin \alpha_2), \\
z_3 &= s_3 (\cos \alpha_3 + i \sin \alpha_3), \\
z_4 &= s_4 (\cos \alpha_4 + i \sin \alpha_4), \\
z_5 &= s_5 (\cos \alpha_5 + i \sin \alpha_5),
\end{align*}
where $s_k > 0$ and $0^\circ \le \alpha_k < 360^\circ.$ Find $\alpha_1 + \alpha_2 + \alpha_3 + \alpha_4 + \alpha_5,$ in degrees.

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