
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 $C: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, the sum of the distances from its upper vertex $B$ to the two foci is $4$, and the eccentricity $e= \frac{\sqrt{3}}{2}$.
(I) Find the equation of ellipse $C$;
(II) If point $A$ is the right vertex of ellipse $C$, and two perpendicular rays are drawn through point $A$, intersecting ellipse $C$ at two distinct points $M$ and $N (M, N$ do not coincide with the left and right vertices), determine whether line $MN$ passes through a fixed point. If it does, find the coordinates of this fixed point; if not, explain why.

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