
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 a moving circle passes through a fixed point F(1, 0) and is tangent to the fixed line l: x = -1.
(1) Find the equation of the trajectory C of the center of the moving circle;
(2) The midpoint of the chord AB, formed by the intersection of line l and C, is (2, 1), and O is the origin. Calculate $$\overrightarrow {OA}\cdot \overrightarrow {OB}$$ and $$|\overrightarrow {AB}|$$.

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