
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
\[ z^6 = -\frac{1}{\sqrt{3}} - i\sqrt{\frac{2}{3}} \]
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 $\phi_1 + \phi_2 + \dots + \phi_6$.

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