
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 $(2\sqrt{6}t$ where $t$ is the parameter$)$, and in the polar coordinate system $(($with the same unit length as the Cartesian coordinate system $(xOy)$, and with the origin $O$ as the pole, and the non-negative semi-axis of $x$ as the polar axis$))$, the equation of circle $C$ is $ρ=6\sin θ$.

(I) Find the Cartesian coordinate equation of circle $C$;

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

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