
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 $\begin{cases}x=1+t\cos α, \\\\ y=2+t\sin α\end{cases}$ where $t$ is a parameter. In the polar coordinate system, which shares the same unit length with the Cartesian coordinate system $(xOy)$ and has the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the equation of circle $C$ is given by $p=6\sin θ$.
(I) Find the Cartesian 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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