
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
\[
e^{11\pi i/120} + e^{31\pi i/120} + e^{-13\pi i/120} + e^{-53\pi i /120} + e^{-73\pi i /120}
\]
and express it in the form \( r e^{i \theta} \), where \( 0 \leq \theta < 2\pi \). Find \(\theta\).

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