
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 points $P( \sqrt {3},1)$, $Q(\cos x,\sin x)$, and $O$ as the origin of coordinates, the function $f(x)= \overrightarrow {OP}\cdot \overrightarrow {QP}$.
(1) Find the analytic expression of function $f(x)$ and its minimum positive period;
(2) If $A$ is an internal angle of $\triangle ABC$, $f(A)=4$, $BC=3$, and the area of $\triangle ABC$ is $\frac {3 \sqrt {3}}{4}$, find the perimeter of $\triangle ABC$.

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