
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 the coordinate system, let the function $f(x)= \overrightarrow{OP} \cdot \overrightarrow{QP}$.  
(I) Find the analytical expression for $f(x)$ and the smallest positive period of $f(x)$.  
(II) If $A$ is an internal angle of $\triangle ABC$, $f(A)=4$, and $BC=3$, find the maximum perimeter of $\triangle ABC$.

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