
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
Consider the equation \(z^6 = -64i\). The solutions to this equation can be expressed in the form:
\[
z_k = r_k (\cos \theta_k + i \sin \theta_k),
\]
for \( k=1, 2, ..., 6 \), where \( r_k > 0 \) and \( 0^\circ \le \theta_k < 360^\circ\). Find the sum \( \theta_1 + \theta_2 + \theta_3 + \theta_4 + \theta_5 + \theta_6 \), in degrees.

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