
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
Suppose $4-4$: Coordinate System and Parametric Equations

In the rectangular coordinate system $xoy$, a curve $C$ is defined by the parametric equations $\begin{cases} x=\sqrt{3}\cos \alpha \ y=\sin \alpha \ \end{cases}\ (\alpha$ is a parameter$)$, and a line $l:x-y-6=0$.
(I) Find a point $P$ on the curve $C$ such that the distance from point $P$ to line $l$ is maximum, and find this maximum value.
(II) A line ${l}_{1}$, which is parallel to line $l$ and passes through point $M(-1,0)$, intersects curve $C$ at points $A$ and $B$. Find the product of the distances from point $M$ to points $A$ and $B$.

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