
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 sum of all angles $\theta_1, \theta_2, \dots, \theta_5$ where each $\theta_k$ is a solution in degrees to the equation
\[ z^5 = -\frac{1}{2} - \frac{\sqrt{3}i}{2}. \]
The roots are expressed as $\text{cis } \theta_k$, with $0^\circ \leq \theta_k < 360^\circ$ for all $1 \leq k \leq 5$.

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