
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 in the Cartesian coordinate system $xOy$, the parametric equation of the conic curve $C$ is $\begin{cases} x=2\cos \theta \\ y=\sin \theta\end{cases}$ (where $\theta$ is the parameter), and the fixed point $A(0, -\sqrt{3})$, $F_{1}$, $F_{2}$ are the left and right foci of the conic curve $C$, respectively. The line $l$ passes through point $A$ and $F_{1}$.  
$(1)$ Find the general equation of the conic curve $C$ and the line $l$;  
$(2)$ Suppose the line $l$ intersects the conic curve $C$ at points $E$ and $F$, find the length of the chord $EF$.

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