
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 rectangular coordinate system $(xOy)$, the parametric equation of line $l$ is $\begin{cases}x=1+t\cdot\cos \alpha \\ y=2+t\cdot\sin \alpha \end{cases} (t \text{ is a parameter})$, and in the polar coordinate system (with the same length unit as the rectangular coordinate system $(xOy)$, and with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis), the equation of curve $C$ is $\rho=6\sin \theta$.

(1) Find the rectangular coordinate equation of curve $C$ and the ordinary equation of line $l$ when $\alpha=\frac{\pi}{2}$;

(2) Suppose curve $C$ intersects line $l$ at points $A$ and $B$, and 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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