
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 polar coordinate system with $O$ as the pole and $Ox$ as the polar axis, and using the same unit of length, the polar equation of curve $C$ is $\rho= \frac {6\cos \theta}{\sin ^{2}\theta }$.  
$(1)$ Convert the polar equation of curve $C$ into a Cartesian coordinate equation, and identify the type of curve;  
$(2)$ If the parametric equation of line $l$ is $\begin{cases} x= \frac {3}{2}+t \\ y= \sqrt {3}t \end{cases}$ (where $t$ is the parameter), and line $l$ intersects curve $C$ at points $A$ and $B$, find $| \overrightarrow{AB}|$

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