
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 center of the ellipse (E) is at the origin of the coordinate system, and one focus of the parabola $x^{2}=-4 \sqrt {5}y$ is a focus of the ellipse (E). A triangle is formed by the two endpoints of the major axis and one endpoint of the minor axis of the ellipse (E), with an area of 6.
(I) Find the equation of the ellipse (E);
(II) If a line (l) with a slope of $\frac{3}{2}$ intersects the ellipse (E) at two distinct points A and B, and point C($\frac{4}{3}$,2), find the equation of the line (l) when the area of triangle ABC is maximum.

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