
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 $$\begin{cases} x=m- \sqrt {2}t \\ y= \sqrt {5}+ \sqrt {2}t\end{cases}$$ ($t$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the non-negative half of the $x$-axis as the polar axis, using the same unit of length as the Cartesian coordinate system. The equation of circle $C$ is $\rho=2\sqrt {5}\sin\theta$, and the length of the chord intercepted by line $l$ on circle $C$ is $\sqrt {2}$.

(I) Find the value of the real number $m$.
(II) Suppose circle $C$ intersects line $l$ at points $A$ and $B$, and point $P$ has coordinates $(m, \sqrt {5})$, where $m>0$. Find the value of $|PA|+|PB|$.

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