
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
\[
\cos \theta_1 \sin \theta_2 + 2\cos \theta_2 \sin \theta_3 + 3\cos \theta_3 \sin \theta_4 + 4\cos \theta_4 \sin \theta_5 + 5\cos \theta_5 \sin \theta_1,
\]
over all real numbers $\theta_1,$ $\theta_2,$ $\theta_3,$ $\theta_4,$ and $\theta_5.$

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