
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 a coordinate system where the polar coordinate system and the rectangular coordinate system $(xOy)$ have the same unit of length, with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis $(.)$. Given that the parameteric equation of line $l$ is $\begin{cases} x=2+\frac{1}{2}t \\ y=\frac{\sqrt{3}}{2}t \end{cases}(t)$ (where $t$ is the parameter), and the polar coordinate equation of curve $C$ is $\rho \sin^{2}\theta =8\cos \theta$ .

(I) Find the rectangular coordinate equation of $C$;

(II) Suppose line $l$ intersects curve $C$ at points $A,B$, find the length of the chord $|AB|$.

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