
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 $f(x)=2\sin x\cos x+2 \sqrt {3}\cos ^{2}x- \sqrt {3},x\in R$
(I) Simplify the analytical expression of the function $f(x)$ and find the smallest positive period of the function $f(x)$;
(II) In acute triangle $\triangle ABC$, if $f(A)=1, \overrightarrow{AB}\cdot \overrightarrow{AC}= \sqrt {2}$, find the area of $\triangle ABC$.

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