
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 $P(\sqrt{3}, 1)$, point $Q(\cos x, \sin x)$, and point $O$ as the coordinate origin, the function is defined as $f(x) = \overrightarrow{OP} \cdot \overrightarrow{QP}$.

(1) Find the smallest positive period of the function $f(x)$;

(2) If $A$ is an internal angle of $\triangle ABC$, $f(A) = 4$, and $BC = 3$, find the maximum value of the perimeter of $\triangle ABC$.

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