
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, the equation of line $l$ is $\sqrt {3}x-y-2\sqrt {3}=0$. Taking the origin as the pole and the positive x-axis as the polar axis, establish the polar coordinate system. The polar equation of curve $C$ is $2\cos \theta=\rho(1-\cos^2 \theta)$.
$(1)$ Give a parametric equation of the line $l$ and the Cartesian equation of curve $C$;
$(2)$ Given that line $l$ intersects curve $C$ at points $A$ and $B$, find the coordinates of the midpoint $N$ of segment $AB$.

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