
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]


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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 point P ( $$\sqrt {3}$$, 1) on the ellipse C.
(1) Find the standard equation of the ellipse C;
(2) A moving straight line l passes through the point (2, 0) and intersects the ellipse C at points A and B. Determine if there exists a fixed point D on the x-axis such that the value of $$\overrightarrow {DA^{2}}$$$$- \overrightarrow {DA}$$$$\cdot \overrightarrow {BA}$$ is constant. If it exists, find the coordinates of the fixed point D; if not, explain the reason.

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