
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]


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In the rectangular coordinate system $xOy$, the parametric equations of the curve $C$ are given by $\begin{cases} x=2\cos\beta \\ y=2\sin\beta +1\end{cases}$ where $\beta$ is a parameter. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of line $l$ is given by $\rho\cos(\alpha - \frac{\pi}{4}) = \sqrt{2}$.

1. Find the polar equation of curve $C$ and the rectangular equation of line $l$.
2. Given that line $l$ intersects curve $C$ at points $M$ and $N$, and intersects the $x$-axis at point $P$, find $|PM|\cdot|PN|$.

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