
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
\[ z^6 = -\frac{1}{2} - \frac{\sqrt{3}i}{2} \]
are \( \text{cis } \phi_1, \text{cis } \phi_2, \dots, \text{cis } \phi_6 \), where \( 0^\circ \le \phi_k < 360^\circ \) for all \( 1 \le k \le 6 \). Find \( \phi_1 + \phi_2 + \dots + \phi_6 \). Give your answer in degrees.

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