
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
\[
\cos \alpha \sin \beta + \cos \beta \sin \gamma + \cos \gamma \sin \delta + \cos \delta \sin \epsilon + \cos \epsilon \sin \alpha,
\]
over all real numbers $\alpha, \beta, \gamma, \delta, \epsilon$.

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