
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
This question is worth 10 points in the elective 4-4: Coordinate System and Parametric Equations.  
In the plane Cartesian coordinate system $xOy$, the curve $C$ is given by $\begin{cases} x= \sqrt {3}\cos \alpha \\ y=\sin \alpha \end{cases}$ (with $\alpha$ as the parameter), and the line $l$: $x-y-6=0$.  
(1) Find a point $P$ on curve $C$ such that the distance from point $P$ to line $l$ is maximized, and find this maximum value;  
(2) A line $l_{1}$ passing through point $M(-1,0)$ and parallel to line $l$ 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