
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 arguments of all eighth roots of the complex number $z^8 = -81i$. Express the roots as $z_k = r_k (\cos \theta_k + i \sin \theta_k)$, where $r_k > 0$ and $0^\circ \le \theta_k < 360^\circ.$

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