
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 roots of the equation
\[ z^9 = -\frac{1}{2} - \frac{\sqrt{3}i}{2} \]
are $\text{cis } \theta_1, \text{cis } \theta_2, \dots, \text{cis } \theta_9$. Determine $\theta_1 + \theta_2 + \dots + \theta_9$ with each $\theta_k$ where \(0^\circ \le \theta_k < 360^\circ\). Give your answer in degrees.

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