
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 $l$: $\begin{cases} x=1+ \frac {1}{2}t \\ y=t+1\end{cases}$ ($t$ is the parameter), with the origin $O$ of the Cartesian coordinate system $xOy$ being the pole and the positive half-axis of the $x$-axis as the polar axis, establish a polar coordinate system using the same length units. The polar equation of curve $C$ is represented by $\rho\sin ^{2}\theta=4\cos \theta$.  
(I) Convert the polar equation of curve $C$ to a Cartesian (rectangular) coordinate equation and identify what type of curve $C$ is.  
(II) If line $l$ intersects curve $C$ at points $A$ and $B$, find the length of $|AB|$.

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