
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
\[z^5 = -\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}}\]
are \( \text{cis } \theta_1, \text{cis } \theta_2, \dots, \text{cis } \theta_5 \) where \(0^\circ \le \theta_k < 360^\circ\) for all \(1 \le k \le 5\). Find \( \theta_1 + \theta_2 + \dots + \theta_5 \). Give your answer in degrees.

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