
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 the ellipse C: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \ (a > b > 0)$$ that passes through the point P(1, $$\frac{\sqrt{3}}{2}$$) with an eccentricity e = $$\frac{\sqrt{3}}{2}$$,
(Ⅰ) Find the standard equation of the ellipse C.
(Ⅱ) Suppose a line l that passes through the point E(0, -2) intersects C at points P and Q; find the maximum value of the area of triangle ΔOPQ.

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