
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 $E$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ passing through the point $(0,1)$, with an eccentricity of $\frac{\sqrt{3}}{2}$.
(I) Find the equation of the ellipse $E$;
(II) Let line $l$: $y = \frac{1}{2}x + m$ intersect with ellipse $E$ at points $A$ and $C$. A square $ABCD$ is constructed with $AC$ as its diagonal. Denote the intersection point of line $l$ and the $x$-axis as $N$. Determine whether the distance between points $B$ and $N$ is constant. If it is, find the value; if not, explain the reason.

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