
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 $z^3 = 8\sqrt{3} - 8i$ can be expressed in the form 
\begin{align*}
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).
\end{align*}
where $r_k > 0$ and $0^\circ \le \theta_k < 360^\circ.$  Find $\theta_1 + \theta_2 + \theta_3,$ in degrees.

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