
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 integers $a$, $b$, $c$, and $d$ such that the expression $\cos x + \cos 5x + \cos 9x + \cos 13x + \cos 17x$ can be written in the form \[a \cos bx \cos cx \cos dx \cos ex.\] Then calculate $a + b + c + d + e$.

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