
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
\[
\cos(\theta_1 + \alpha) \sin (\theta_2 + \alpha) + \cos(\theta_2 + \alpha) \sin (\theta_3 + \alpha) + \cos(\theta_3 + \alpha) \sin (\theta_4 + \alpha) + \cos(\theta_4 + \alpha) \sin (\theta_5 + \alpha) + \cos(\theta_5 + \alpha) \sin (\theta_1 + \alpha),
\]
over all real numbers $\theta_1,$ $\theta_2,$ $\theta_3,$ $\theta_4,$ $\theta_5,$ and for a fixed real number $\alpha.$

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