
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
Evaluate the complex number
\[e^{11\pi i/60} + e^{29\pi i/60} + e^{49 \pi i/60} + e^{59\pi i /60} + e^{79 \pi i /60}\]
and find the argument $\theta$ where the expression is in the form $r e^{i \theta}$ and $0 \le \theta < 2\pi$.

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