
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 $xOy$, a line $l$ is described by the parametric equations $\begin{cases} x = 1 + \frac{\sqrt{2}}{2}t \\ y = 2 + \frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter). In the polar coordinate system, using the same length units as the Cartesian coordinate system and with the origin $O$ as the pole and the positive $x$-axis as the polar axis, the equation of circle $C$ is given by $\rho = 6\sin\theta$.
(Ⅰ) Find the standard equation of circle $C$ in the Cartesian coordinate system;
(Ⅱ) If point $P(l, 2)$ exists, 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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