
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 W: $$\frac {x^{2}}{4}+ \frac {y^{2}}{b^{2}}=1$$ (where $b>0$) has one of its foci at $$(\sqrt{3}, 0)$$.
(I) Find the equation of ellipse W and its eccentricity;
(II) If ellipse W intersects the y-axis at points A and B (with A above B), M is any point on the ellipse other than A and B. A line through M perpendicular to the y-axis intersects at N, E is the midpoint of segment MN, line AE intersects line $y=-1$ at point C, G is the midpoint of segment BC, and O is the origin. Find the measure of $\angle OEG$.

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