
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 $\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$ ($a > b > 0$) and a line $l: y = -\frac { \sqrt {3}}{3}x + b$ intersect at two distinct points P and Q. The distance from the origin to line $l$ is $\frac { \sqrt {3}}{2}$, and the eccentricity of the ellipse is $\frac { \sqrt {6}}{3}$.

(Ⅰ) Find the equation of the ellipse;  
(Ⅱ) Determine whether there exists a real number $k$ such that the line $y = kx + 2$ intersects the ellipse at points P and Q, and the circle with diameter PQ passes through point D(1, 0). If it exists, find the value of $k$; if not, explain why.

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