
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 point P whose distance to a fixed point $$F( \sqrt {2}, 0)$$ is in the ratio of $$\frac { \sqrt {2}}{2}$$ to its distance to a fixed line $$l: x=2 \sqrt {2}$$.

(1) Find the equation of the trajectory C of the moving point P;  
(2) Let M and N be two points on the line l, and point E is symmetric to point F with respect to the origin O. If $$\overrightarrow {EM} \cdot \overrightarrow {FN} = 0$$, find the minimum value of |MN|.

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