
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 equations for line $l$: $$\begin{cases} x=2+t \\ y=2t \end{cases}$$ (where $t$ is a parameter), and establishing a polar coordinate system with the origin $O$ of the Cartesian coordinate system xOy as the pole and the Ox-axis as the polar axis with the same unit length, the polar equation of curve $C$ is obtained as $\rho = \frac{8\cos\theta}{\sin^2\theta}$.
(1) Convert the polar equation of curve $C$ into a Cartesian coordinate equation and identify the type of curve it represents.
(2) 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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