
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 vectors $\overrightarrow{a}=(2\cos x,\sin x-\cos x)$ and $\overrightarrow{b}=( \sqrt {3}\sin x,\sin x+\cos x)$, define a function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}$.

(I) Find the expression for $f(x)$ and the set of values for $x$ when $f(x)$ reaches its maximum.
(II) In triangle $ABC$, if the corresponding sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ satisfy $a+b=2 \sqrt {3}$, $c= \sqrt {6}$, and $f(C)=2$, find the area of triangle $ABC$.

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