
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 $W$: $\dfrac{x^2}{4} + \dfrac{y^2}{b^2} = 1 (b > 0)$ has a focus at $(\sqrt{3}, 0)$.

(Ⅰ) Find the equation and eccentricity of the ellipse $W$;

(Ⅱ) If the ellipse $W$ intersects the $y$-axis at points $A$ and $B$ (point $A$ is above point $B$), $M$ is any point on the ellipse other than $A$ and $B$. A line through point $M$ 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}
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