
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 angle $\theta$ such that the expression 
\[e^{11\pi i/60} + e^{23\pi i/60} + e^{35 \pi i/60} + e^{47\pi i /60} + e^{59 \pi i /60} + e^{\pi i /60}\]
can be expressed in the form $r e^{i \theta}$, where $0 \le \theta < 2\pi$.

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