
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 $$\begin{cases} x=2+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t \end{cases}$$ (where $t$ is the parameter), in the polar coordinate system with the origin as the pole and the positive x-axis as the polar axis (with the same unit length), the polar equation of curve $C$ is $\rho\sin^2\theta=8\cos\theta$.  
(1) Find the Cartesian coordinate equation of curve $C$;  
(2) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the length of chord $|AB|$.

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