
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 the angles \(\theta_1, \theta_2, \dots, \theta_6\) for the roots of the equation:
\[ z^6 = -1 - i, \]
where the roots are \( \text{cis } \theta_1, \text{cis } \theta_2, \dots, \text{cis } \theta_6 \) with \(0^\circ \le \theta_k < 360^\circ\) for all \(1 \le k \le 6\). Answer in degrees.

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