
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
Consider the ellipse E: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ (where $a > b > 0$) with foci $F_1$ and $F_2$ on the left and right, respectively.
(I) If the major axis, minor axis, and the focal distance of ellipse E form an arithmetic sequence, find the eccentricity of ellipse E.
(II) If ellipse E passes through point A(0, -2), and the lines $AF_1$ and $AF_2$ intersect the ellipse at points B and C respectively, and the area of triangle ABC is $$\frac{50c}{9}$$, find the equation of ellipse E.

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