
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 $\begin{cases} x=1+\dfrac{\sqrt{2}}{2}t \\ y=2+\dfrac{\sqrt{2}}{2}t \end{cases}$ ($t$ is the parameter), in the polar coordinate system (with the same unit length as the Cartesian coordinate system $xOy$, and the origin $O$ as the pole, and the non-negative half-axis of $x$ as the polar axis), the equation of circle $C$ is $\rho=6\sin\theta$.
- (I) Find the standard equation of circle $C$ in Cartesian coordinates;
- (II) If point $P(l,2)$, suppose 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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