
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
\[
\cos (\theta_1 + \phi) \sin (\theta_2 + \phi) + \cos (\theta_2 + \phi) \sin (\theta_3 + \phi) + \cos (\theta_3 + \phi) \sin (\theta_4 + \phi) + \cos (\theta_4 + \phi) \sin (\theta_5 + \phi) + \cos (\theta_5 + \phi) \sin (\theta_1 + \phi),
\]
where $\phi$ is a fixed real number and $\theta_1, \theta_2, \theta_3, \theta_4, \theta_5$ are variables.

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