
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 $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ with eccentricity $$e= \frac { \sqrt {6}}{3}$$, and the line $y=bx+2$ is tangent to the circle $x^{2}+y^{2}=2$.  
(1) Find the equation of the ellipse;  
(2) Given the fixed point E(1,0), if the line $y=kx+2$ ($k\neq0$) intersects the ellipse at points C and D, determine whether there exists a real number $k$ such that the circle with CD as its diameter passes through the fixed point E. 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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