
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 polar coordinate system, the coordinates of the center of circle $C$ are $C(2, \frac{π}{3})$, with a radius of $2$. Establish a plane rectangular coordinate system with the pole as the origin and the positive half of the $x$-axis as the polar axis, using the same unit of length. The parametric equations of line $l$ are $ \begin{cases} x=1- \frac{ \sqrt {3}}{2}t \\ y= \sqrt {3}+ \frac{1}{2}t \end{cases}(t \text{ is the parameter}) $
(I) Find the polar coordinate equation of circle $C$;
(II) Suppose the intersection points of line $l$ and circle $C$ are $A$ and $B$, and the intersection point of line $l$ and the $x$-axis is $P$. Find $|PA|+|PB|$.

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