
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 $f(x) = 2\sqrt{3}\sin x\cos x - 2\cos^2 x + 1$.
1. Find the set of values of $x$ when the function $f(x)$ reaches its maximum value;
2. Let $\triangle ABC$ have angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively. If $f(C) = 2$ and $c = \sqrt{3}$, find the maximum area of $\triangle ABC$.

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