
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 equations of the curve $C$ are given by $\begin{cases} x=\sqrt{3}\cos\theta \\ y=\sin\theta \end{cases}$ ($\theta$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of the straight line $l$ is $\rho\sin(\theta+\frac{\pi}{4})=1$. The line $l$ intersects the curve $C$ at points $A$ and $B$.
(1) Find the rectangular coordinate equation of the line $l$;
(2) If the line $l$ intersects the $y$-axis at point $P$, find $|PB|\cdot|PA|$.

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