
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
The expression $\cos x + \cos 5x + \cos 11x + \cos 15x$ can be rewritten in the equivalent form
\[a \cos bx \cos cx \cos dx\]
for some positive integers $a,$ $b,$ $c,$ and $d.$ Determine $a + b + c + d.$

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