
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 the sum of the angles of the solutions in degrees to the equation $w^4 = 81i$. Express the solutions in the form:
\[
w_1 = r_1 (\cos \theta_1 + i \sin \theta_1),
\]
\[
w_2 = r_2 (\cos \theta_2 + i \sin \theta_2),
\]
\[
w_3 = r_3 (\cos \theta_3 + i \sin \theta_3),
\]
\[
w_4 = r_4 (\cos \theta_4 + i \sin \theta_4),
\]
where $r_k > 0$ and $0^\circ \le \theta_k < 360^\circ.$

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