
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
In the Cartesian coordinate plane $(xOy)$, a curve $C$ is defined by the parametric equations $\begin{cases} x = \sqrt{3}\cos\alpha \\ y = \sin\alpha \end{cases}$ and a line $l$ is defined by the equation $x - y - 6 = 0$.

1. Find a point $P$ on the curve $C$ such that the distance from $P$ to the line $l$ is maximized, and compute this maximum distance.
2. A line $l_1$ parallel to $l$ passes through the point $M(-1, 0)$ and intersects the curve $C$ at points $A$ and $B$. Compute the product of the distances from $M$ to $A$ and $B$.

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