
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 $(xOy)$, line $l$ passes through the point $(3, \sqrt {5})$ with an angle of inclination of $\frac {\pi}{4}$. In the polar coordinate system, which has the same unit length and origin $O$ as the Cartesian system and the positive semi-axis of $x$ as the polar axis, the equation of circle $C$ is $p=2 \sqrt {5}\sin θ$.
(1) Find the parametric equation of line $l$ and the rectangular equation of circle $C$;
(2) Suppose circle $C$ intersects line $l$ at points $A$ and $B$, and point $P$ has coordinates $(3, \sqrt {5})$, find $|PA| \cdot |PB|$.

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