
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 the function $f(x)=2 \sqrt {3}\sin x\cos x+2\cos ^{2}x$, and the sides $a$, $b$, $c$ opposite to the angles $A$, $B$, $C$ of $\triangle ABC$ respectively, with $a=2 \sqrt {3}$.
(1) Find the maximum value of $f(x)$ and the set of corresponding $x$ values where this maximum is achieved;
(2) If $f(A)=2$, $b+c=6$, find the area of $\triangle ABC$.

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