
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 given by
$$
\begin{cases}
x = 1 + t\cos\alpha \\
y = 2 + t\sin\alpha
\end{cases}
$$
where $t$ is the parameter. In the polar coordinate system, which uses the same unit length as $xOy$ and has the origin $O$ as the pole and the positive $x$-axis as the polar axis, the equation of circle $C$ is $\rho = 6\sin\theta$.
(I) Find the Cartesian coordinate equation of circle $C$.
(II) Suppose circle $C$ intersects line $l$ at points A and B. If point P has coordinates (1, 2), find the minimum value of $|PA|+|PB|$.

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