
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), and its eccentricity is $\frac{\sqrt{3}}{2}$.
(I) Find the equation of ellipse E;
(II) Let line l: $y = \frac{x}{2} + m$ intersect the ellipse E at points A and C, and suppose a square ABCD is formed with AC as its diagonal. If line l intersects the x-axis at point N, is the distance between points B and N constant? If so, determine the value; if not, provide a reason.

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