
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 $xOy$, with $O$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of circle $C$ is $\rho=4\sin \theta$, and the parametric equation of line $l$ is $\begin{cases} & x=-\dfrac{\sqrt{3}}{2}t \\ & y=2+\dfrac{t}{2} \\ \end{cases}$ (where $t$ is the parameter), line $l$ intersects circle $C$ at points $A$ and $B$.

(Ⅰ) Find the polar coordinates of the center of the circle;

(Ⅱ) The intersection of line $l$ and the $x$-axis is point $P$, find $|PA|+|PB|$.

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