
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: $$\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$), and the shortest distance from a point on the ellipse to one of its foci is $$\frac { \sqrt {3}}{3}b$$.

(Ⅰ) Find the eccentricity of ellipse C;

(Ⅱ) If point M ($$\sqrt {3}$$, $$\frac { \sqrt {3}}{2}$$) is on ellipse C, and a line l not passing through the origin O intersects ellipse C at points A and B, and intersects line OM at point N, with N being the midpoint of segment AB, find the maximum area of triangle OAB.

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