
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 E: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (a>b>0), its right focus F coincides with the focus of the parabola y=4x, and the eccentricity of the ellipse is $$\frac {1}{2}$$.
(I) Find the standard equation of the ellipse;
(II) Does there exist a point M on the x-axis such that the dot product of $$\overrightarrow {MA}$$ and $$\overrightarrow {MB}$$ is a constant, where A and B are the intersection points of the line l passing through the right focus F of the ellipse E and the ellipse itself? If it exists, find the coordinates of point M; if not, explain the reason.

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