
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$) with an eccentricity of $$\frac { \sqrt {6}}{3}$$, and a circle centered at the origin O with the major axis of ellipse C as its radius is tangent to the line $2x- \sqrt {2}y+6=0$.  
(1) Find the standard equation of ellipse C;  
(2) Given that points A and B are the two intersection points of the moving line $y=k(x-2)$ ($k\neq0$) with ellipse C, is there a point E on the x-axis such that $\overrightarrow {EA}^{2}+ \overrightarrow {EA} \cdot \overrightarrow {AB}$ is a constant value? If it exists, find the coordinates of point E and the constant value; if not, explain why.

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