
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 $$\frac {\sqrt {2}}{2}$$, and point P(1, $$\frac {\sqrt {2}}{2}$$) lies on ellipse C. Line 1 passes through the right focus of the ellipse and intersects the ellipse at points A and B.  
(1) Find the equation of ellipse C;  
(2) Is there a fixed point M on the x-axis such that $$\overrightarrow {MA} \cdot \overrightarrow {MB}$$ is a constant value? If it exists, find the coordinates of point M; if not, explain why.

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