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

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