
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]


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Given an ellipse C: $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 (a > b > 0) with an eccentricity of $$\frac { \sqrt {2}}{2}$$, the length of the line segment obtained by intersecting the line y = 1 with the ellipse C is 2$$\sqrt {2}$$.
(I) Find the equation of the ellipse C;
(II) Let line l intersect with ellipse C at points A and B, point D is on the ellipse C, and O is the coordinate origin. If $$\overrightarrow {OA}$$ + $$\overrightarrow {OB}$$ = $$\overrightarrow {OD}$$, determine whether the area of the quadrilateral OADB is a fixed value. If it is, find the fixed value; if not, explain the reason.

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