
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 sides of an isosceles triangle are $\cos x,$ $\cos x,$ and $\cos 9x,$ with its vertex angle as $3x.$ (All angle measurements are in degrees.) Determine all possible values of $x,$ separated by commas.

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