
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 system xOy, it is known that the normal equation of line $l$ is $x-y-2=0$, and the parametric equation of curve $C$ is:
$$
\begin{cases}
x = 2\sqrt{3}\cos\theta \\
y = 2\sin\theta
\end{cases}
$$
where $\theta$ is the parameter. Let line $l$ intersect curve $C$ at points A and B.
(1) Find the length of the line segment AB.
(2) Point P moves on curve C. When the area of $\triangle PAB$ is maximal, find the coordinates of point P and the maximum area of $\triangle PAB$.

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