The expression $\cos x + \cos 3x + \cos 7x + \cos 9x$ can be written in the equivalent form
\[a \cos bx \cos cx \cos dx\]for some positive integers $a,$ $b,$ $c,$ and $d.$  Find $a + b + c + d.$
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<|im_start|>user
The expression $\cos x + \cos 3x + \cos 7x + \cos 9x$ can be written in the equivalent form
\[a \cos bx \cos cx \cos dx\]for some positive integers $a,$ $b,$ $c,$ and $d.$  Find $a + b + c + d.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
13
The expression $\cos x + \cos 3x + \cos 7x + \cos 9x$ can be written in the equivalent form
\[a \cos bx \cos cx \cos dx\]for some positive integers $a,$ $b,$ $c,$ and $d.$  Find $a + b + c + d.$
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