
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 fixed point A(1, 0) and two moving points E, F on the fixed line x=-1, satisfying $$\overrightarrow {AE}\perp \overrightarrow {AF}$$, the moving point P satisfies $$\overrightarrow {EP}\parallel \overrightarrow {OA}$$, $$\overrightarrow {FO}\parallel \overrightarrow {OP}$$ (where O is the origin).  
(1) Find the equation of the trajectory C of the moving point P;  
(2) A line l passing through point B(0, 2) intersects the trajectory C at two different points M, N. If $$\overrightarrow {AM}\cdot \overrightarrow {AN}<0$$, find the range of the slope of line l.

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