
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 that point P moves on the circle O: x²+y²=6, and the projection of point P on the x-axis is Q. The moving point M satisfies $(1- \sqrt {3}) \overrightarrow {OQ}= \overrightarrow {OP}- \sqrt {3} \overrightarrow {OM}$.
(1) Find the equation of the trajectory E of the moving point M.
(2) The moving straight line l passes through the point (2,0) and intersects the curve E at points A and B. Is there a fixed point D on the x-axis such that the value of $\overrightarrow {DA}\cdot \overrightarrow {AB}+ \overrightarrow {DA}^{2}$ is constant? If it exists, find the coordinates of the fixed point D and the constant value; if not, explain the reason.

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