
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
In the Cartesian coordinate system, with the origin as the pole and the positive half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. It is known that the curve $C$: $\rho^{2}= \frac {12}{2+\cos ^{2}\theta}$, and the line $l$: $2\rho\cos (\theta- \frac {\pi}{6})= \sqrt {3}$.
$(1)$ Write the parametric equation of the line $l$;
$(2)$ Suppose the line $l$ intersects the curve $C$ at two points $A$ and $B$, find the value of $|AB|$.

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