
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 \( z^6 = 64i \) can be expressed in the form
\[
z_1 = r_1 (\cos \theta_1 + i \sin \theta_1), \\
z_2 = r_2 (\cos \theta_2 + i \sin \theta_2), \\
z_3 = r_3 (\cos \theta_3 + i \sin \theta_3), \\
z_4 = r_4 (\cos \theta_4 + i \sin \theta_4), \\
z_5 = r_5 (\cos \theta_5 + i \sin \theta_5), \\
z_6 = r_6 (\cos \theta_6 + i \sin \theta_6),
\]
where \( r_k > 0 \) and \( 0^\circ \le \theta_k < 360^\circ \). Find \( \theta_1 + \theta_2 + \theta_3 + \theta_4 + \theta_5 + \theta_6 \), in degrees.

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