
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.
(2) Let $\triangle ABC$'s angles $A$, $B$, and $C$ correspond to the sides $a$, $b$, and $c$ respectively. If $f(C)=2$, $c= \sqrt {3}$, find the maximum area of $\triangle ABC$.

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