
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
(Selective 4-4: Coordinate System and Parametric Equations) In the Cartesian coordinate system $xoy$, the parametric equation of line $l$ is $$\begin{cases} x=3- \frac { \sqrt {2}}{2}t \\ y= \sqrt {5}+ \frac { \sqrt {2}}{2}t \end{cases}$$ (where $t$ is the parameter). In the polar coordinate system (using the same unit length as the Cartesian coordinate system $xoy$, and taking the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis), the equation of circle $C$ is $$\rho=2 \sqrt {5}\sin\theta$$.
(Ⅰ) Find the Cartesian coordinate equation of circle $C$;
(Ⅱ) Suppose circle $C$ intersects line $l$ at points $A$ and $B$. If the coordinates of point $P$ are $(3, \sqrt {5})$, find $|PA|+|PB|$.

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