
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 equation of line $l$ is $$\begin{cases} x=3- \frac { \sqrt {2}}{2}t \\ y= \sqrt {5}- \frac { \sqrt {2}}{2}t\end{cases}$$ ($t$ is the parameter). In the polar coordinate system (with the same length unit as the rectangular coordinate system $xOy$, and with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis), the equation of circle $C$ is $\rho=2\sqrt {5}\sin\theta$.

(I) Find the rectangular coordinate equation of circle $C$;

(II) Suppose circle $C$ intersects line $l$ at points $A$ and $B$, and point $P$ has coordinates $(3,\sqrt {5})$. Find $\frac {1}{|PA|}+\frac {1}{|PB|}$.

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