
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 solutions to \(z^6 = 64i\) and calculate the sum of their angles in degrees. Express each solution \(z_k\) in the form
\begin{align*}
z_k = r_k (\cos \theta_k + i \sin \theta_k),
\end{align*}
where \(r_k > 0\) and \(0^\circ \leq \theta_k < 360^\circ.\) Then find the sum \(\theta_1 + \theta_2 + \theta_3 + \theta_4 + \theta_5 + \theta_6.\)

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