
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
Coordinate System and Parametric Equations

In the rectangular coordinate system $(xOy)$, the parametric equation of line $l$ is $\begin{cases}x=\frac{1}{2}t \\ y=1-\frac{\sqrt{3}}{2}t\end{cases} (t$ is the parameter$)$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of circle $C$ is $\rho=2\sin \theta$.

(I) Determine the number of intersection points between line $l$ and circle $C$;

(II) If circle $C$ intersects with line $l$ at points $A$ and $B$, find the length of line segment $AB$.

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