
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
A focus of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\frac{\sqrt{3}}{2}$ coincides with the center of the circle ${x^2} + 2\sqrt{3}x + {y^2} = 0$.
(I) Find the equation of ellipse $E$;
(II) Let $A$ be the upper vertex of the ellipse $E$, and let a line with slope $k (k > 0)$ intersect $E$ at points $A$ and $M$, while point $N$ lies on $E$ and $MA \perp NA.$ Determine whether line $MN$ passes through a fixed point. If it does, find the coordinates of this fixed point; if not, explain the reason.

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