
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, a polar coordinate system is established with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The parametric equations of the curve $C$ are given by $\begin{cases} x=2\cos \alpha \\ y=3\sin \alpha \end{cases}\ (\alpha$ is the parameter$)$, and the polar coordinate equation of the line $l$ is $\rho\cos \theta-2\rho\sin \theta-4=0$.

(1) Find the rectangular coordinate equation of line $l$ and the general equation of curve $C$;

(2) If the intersection of line $l$ and the $x$-axis is point $A$, and the intersections of line $l$ and curve $C$ are points $B$ and $D$, find the value of $|AB|\cdot|AD|$.

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