
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 parametric equation of line $l$ as 
$$\begin{cases} 
x= \frac{1}{2}t, \\ 
y= \frac{\sqrt{3}}{2}t+1
\end{cases}
(t \text{ is the parameter}),$$
and the parametric equation of curve $C$ as
$$\begin{cases}
x=2+\cos \theta, \\ 
y=\sin \theta
\end{cases}
(\theta \text{ is the parameter}),$$
(I) It is known in the polar coordinate system (where the same length unit is shared with the Cartesian coordinate system $xOy$, and the origin $O$ is the pole, with the positive half-axis of $x$ as the polar axis), the polar coordinate of point $P$ is $(4, \frac{\pi}{3})$. Determine the positional relationship of point $P$ with the line $l$.

(II) Let point $Q$ be a moving point on curve $C$. Find the minimum and maximum values of the distance from point $Q$ to line $l$.

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