
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 point $A(0,-2)$, ellipse $E$: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 (a > b > 0)$ has an eccentricity of $\frac{\sqrt{3}}{2}$. $F$ is the right focus of ellipse $E$, and the slope of line $AF$ is $\frac{2\sqrt{3}}{3}$. $O$ is the origin.<br/>$(1)$ Find the equation of $E$;<br/>$(2)$ Let the moving line $l$ passing through point $A$ intersect $E$ at points $P$ and $Q$. When the area of $\triangle OPQ$ is equal to $1$, find the equation of $l$.

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