
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 a curve C with the polar coordinate equation $ρ = \frac{\cos θ}{\sin^2 θ}$ in the rectangular coordinate system $xOy$ with $O$ as the pole and $Ox$ as the polar axis, using the same unit length to establish the polar coordinate system.

(1) Convert the polar coordinate equation of the curve C to a rectangular coordinate equation and identify the type of curve.

(2) If the parameter equation of line $l$ is given by $\begin{cases} x = \frac{3}{2} + t \\ y = \sqrt{3}t \end{cases}$ (where $t$ is the parameter), find the distance $|AB|$ between points $A$ and $B$ where line $l$ intersects curve $C$.

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