
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 $$\overrightarrow {a} = (x-1, y)$$, $$\overrightarrow {b} = (x+1, y)$$, and $$|\overrightarrow {a}| + |\overrightarrow {b}| = 4$$  
(1) Find the equation of the trajectory C of point M(x, y).  
(2) Let P be a moving point on curve C, and F<sub>1</sub>(-1, 0), F<sub>2</sub>(1, 0), find the maximum and minimum values of $$\overrightarrow {PF_{1}} \cdot \overrightarrow {PF_{2}}$$.  
(3) If a line l intersects curve C at points A and B, and a circle with AB as its diameter passes through the origin O, investigate whether the distance from point O to line l is constant. If yes, find the constant value; if no, explain why.

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