
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
Given the parametric equation of line $l$ as $ \begin{cases} x=4+ \frac{1}{2}t \\ y= \frac{ \sqrt{3}}{2}t \end{cases} (t \text{ is the parameter})$, establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of curve $C$ is $ρ=2\cos θ$.
(I) Find the rectangular coordinate equation of curve $C$ and the polar coordinate equation of line $l$.
(II) If line $θ= \frac{π}{6}$ intersects curve $C$ at point $A$ (which is not the origin) and intersects line $l$ at point $B$, find the value of $|AB|$.

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