
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 maximum value of
\[
\sin (\theta_1 + \theta_2) - \sin (\theta_1 - \theta_2) + \sin (\theta_2 + \theta_3) - \sin (\theta_2 - \theta_3) + \sin (\theta_3 + \theta_4) - \sin (\theta_3 - \theta_4) + \sin (\theta_4 + \theta_5) - \sin (\theta_4 - \theta_5) + \sin (\theta_5 + \theta_1) - \sin (\theta_5 - \theta_1),
\]
over all real numbers $\theta_1, \theta_2, \theta_3, \theta_4, \theta_5.$

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