
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 the ellipse $E$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity of $\frac{\sqrt{3}}{2}$, $F$ is the right focus of the ellipse, point $A(0,-2)$, and the slope of line $AF$ is $\frac{2\sqrt{3}}{3}$, $O$ is the coordinate origin.

(1) Find the equation of ellipse $E$;

(2) Line $l$ passes through point $A$ with a slope angle of $\frac{2\pi}{3}$ and intersects $E$ at points $P$ and $Q$, find the area of $\triangle OPQ$.

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