
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 $A$, $B$, and $C$ are the angles opposite to sides $a$, $b$, and $c$ of $\triangle ABC$ respectively, and the area of $\triangle ABC$ is $S$. It is also given that $\sqrt{3}\overrightarrow{CA} \cdot \overrightarrow{CB} = 2S$.  
(I) Find the measure of angle $C$;  
(II) If $c = \sqrt{6}$, find the maximum perimeter of $\triangle ABC$.

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