
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 $\begin{cases}x=\cos \theta \
y=2+\sin \theta\end{cases} (\theta \text{ is the parameter })$
(I) In the polar coordinate system with the same unit length as the rectangular coordinate system $xOy$, and taking the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the polar coordinates of point $P$ are $(4, \frac{ \pi }{6})$. Determine the positional relationship between point $P$ and 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}
user