
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 $xOy$, the parametric equation of line $l$ is $\begin{cases} x=1+ \sqrt {2}t \\ y= \sqrt {2}t\end{cases}$ (where $t$ is the parameter), and in the polar coordinate system with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C$ is $3\rho^{2}\cos ^{2}\theta+4\rho^{2}\sin ^{2}\theta=12$, and line $l$ intersects curve $C$ at points $P$ and $Q$.  
(I) Find the general equation of line $l$ and the Cartesian coordinate equation of curve $C$;  
(II) Denote the intersection point of line $l$ with the $x$-axis as $A$, and calculate the value of $|AP|\cdot|AQ|$.

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