
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
Calculate $\theta_1 + \theta_2 + \theta_3 + \theta_4$ for the complex equation $z^4 = 16i$, where each solution can be expressed as:
\[
z_k = r_k (\cos \theta_k + i \sin \theta_k),
\]
and $r_k > 0$ and $0^\circ \leq \theta_k < 360^\circ$ for $k=1, 2, 3, 4$.

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