
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 equations of a line are given by $x=3-\frac{\sqrt{2}}{2}t$ and $y=\sqrt{5}+\frac{\sqrt{2}}{2}t$. In the polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the equation of circle $C$ is $p=2\sqrt{5}\sin\theta$.

(I) Write the standard equation of the line and the rectangular coordinate equation of circle $C$.

(II) If the rectangular coordinates of point $P$ are $(3,\sqrt{5})$, and circle $C$ intersects with line $l$ at points $A$ and $B$, find the value of $|PA|+|PB|$.

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