
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]


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In the Cartesian coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x=1+t\cos α \\ y=2+t\sin α \end{cases} (t \text{ is the parameter})$, and in the polar coordinate system (with the same unit length as the Cartesian coordinate system $(xOy)$, taking the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis), the equation of circle $C$ is $ρ=6\sin θ$.

(1) Find the Cartesian equation of circle $C$.
(2) If point $P(1,2)$, and circle $C$ intersects line $l$ at points $A$ and $B$, find the minimum value of $|PA|+|PB|$.

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