
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, 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, with the origin O as the pole and the positive x-axis as the polar axis), the equation of the circle $C$ is 
$$
ρ=2 \sqrt {5}\sinθ.
$$
(I) Find the distance from the center of the circle $C$ to the line $l$.
(II) Assume that circle $C$ intersects line $l$ at points $A$ and $B$. If point $P$ has coordinates $(3, \sqrt {5})$, find $|PA|+|PB|$.

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