
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 rectangular coordinate system $xOy$, the parametric equation of line $l$ is $$\left\{\begin{array}{l}x=1+t \\ y=1−t\end{array}\right.$$ ($t$ is the parameter), and the polar coordinate system is established with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho^2(5-4\cos2\theta)=9$, and line $l$ intersects curve $C$ at points $A$ and $B$.
(1) Find the general equation of line $l$ and the rectangular equation of curve $C$;
(2) If the polar coordinates of point $P$ are $(\sqrt{2}, \frac{3\pi}{4})$, find the area of $\triangle PAB$.

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