
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: $\begin{cases}x=1+t\cos α \\ y=2+t\sin α\end{cases}$ ($t$ is a parameter, $0\leqslant α\leqslant π $). Establish a polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of the curve $C$ is $ρ=6\sin θ$.

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

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