
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 an ellipse (C) with the equation $ \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, its eccentricity is $\frac{\sqrt{3}}{2}$, and the area of the rhombus formed by its four vertices is 4.
(I) Find the equation of the ellipse;
(II) The quadrilateral ABCD has its vertices on the ellipse (C), and its diagonals AC and BD pass through the origin O. If $k_{AC} \cdot k_{BD} = -\frac{1}{4}$,
(i) Find the range of $ \overrightarrow{OA} \cdot \overrightarrow{OB}$;
(ii) Find the area of the quadrilateral ABCD.

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