
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 that the short axis of the ellipse $E: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a>b>0)$ is 2, and the eccentricity is $\frac{\sqrt{3}}{2}$.
1. Find the equation of the ellipse E;
2. If the right focus and the right vertex of ellipse E are F and C respectively, and the line passing through F intersects the ellipse at points A and B, find the maximum area of the quadrilateral OACB (O is the coordinate origin).

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