
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 equations of line $l$ are given by $\begin{cases} x=1+\frac{\sqrt{2}}{2}t \\ y=2+\frac{\sqrt{2}}{2}t \end{cases}$ ($t$ is the parameter). In the polar coordinate system that uses the same unit length and has the origin $O$ as the pole and the non-negative half of the $x$-axis as the polar axis, the equation of circle $C$ is $\rho=6\sin\theta$.

(I) Find the standard equation of circle $C$ in the Cartesian coordinate system.
(II) If point $P(l, 2)$, and circle $C$ intersects 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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