
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 point P ($\sqrt{3}$, 1), Q (cos x, sin x), and O as the origin, let the function $f(x) = \overrightarrow{OP} \cdot \overrightarrow{QP}$.
(1) Find the minimum value of the function $f(x)$ and the corresponding value of x;
(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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