
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
Given the parametric equation of line $l$ as $\begin{cases}x=-\frac{1}{2}+\frac{\sqrt{2}}{2}t \\ y=\frac{1}{2}+\frac{\sqrt{2}}{2}t\end{cases}$ and the parametric equation of ellipse $C$ as $\begin{cases}x=2\cos\theta \\ y=\sqrt{3}\sin\theta\end{cases}$, in a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the polar coordinates of point $A$ are $(\frac{\sqrt{2}}{2},\frac{3}{4}\pi)$.

(1) Convert the coordinates of point $A$ to rectangular coordinates and convert the parametric equation of the ellipse to a standard form.
(2) Line $l$ intersects ellipse $C$ at points $P$ and $Q$. Find the value of $|AP|\cdot|AQ|$.

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