
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 sum of the two smallest possible values of  $x^\circ$  (in degrees) that satisfy the following equation if  $x$  is greater than  $2017^\circ$ :   $$ \cos^59x+\cos^5x=32\cos^55x\cos^54x+5\cos^29x\cos^2x\left(\cos9x+\cos x\right). $$  *2017 CCA Math Bonanza Individual Round #10*

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