
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 $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, passing through the point $(1, \frac{\sqrt{3}}{2})$ and having an eccentricity of $\frac{\sqrt{3}}{2}$. Point A is the right vertex of ellipse C, and the line l intersects the ellipse at two points P($x_1, y_1$) and Q($x_2, y_2$) distinct from A.

(I) Find the standard equation of ellipse C;
(II) When $\overrightarrow{AP} \bullet \overrightarrow{AQ} = 0$, find the maximum area of triangle OPQ.

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