
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 $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1$ ($a > b > 0$) passing through point $P(1, \frac{\sqrt{3}}{2})$ with eccentricity $e= \frac{\sqrt{3}}{2}$
(I) Find the standard equation of ellipse $C$.
(II) Let line $l$ pass through point $E(0, -2)$ intersecting $C$ at points $P$ and $Q$. Find the maximum area of $\triangle OPQ$.

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