
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
Determine the angles $\theta_1, \theta_2, \theta_3, \theta_4$ such that the solutions to $z^4 = 32i$ can be expressed in terms of $r_k$ and $\theta_k$ where $r_k > 0$ and $0^\circ \le \theta_k < 360^\circ$. Then, find $\theta_1 + \theta_2 + \theta_3 + \theta_4$ in degrees.

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