
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) with the equation $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, its eccentricity is $\frac{\sqrt{3}}{2}$, the right vertex is A, the lower vertex is B, and the point $P(\frac{3}{4}, 0)$ satisfies $|PA| = |PB|$.
(I) Find the equation of the ellipse (C).
(II) A line $l$ that is not perpendicular to the coordinate axis intersects with the ellipse (C) at points M and N. A circle passes through the origin with $MN$ as its diameter, and the perpendicular bisector of line segment $MN$ passes through point $P$. Find the equation of line $l$.

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