
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
Given that $a, b, c$ are the sides opposite to angles $A, B, C$ respectively in $\triangle ABC$, and $\cos A \sin B \sin C + \cos B \sin A \sin C = 2 \cos C \sin A \sin B$, find the maximum value of $C$.

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