
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 and two fixed points $$A(- \sqrt {2}, 0), B( \sqrt {2}, 0)$$ on a plane, the product of the slopes of the lines connecting P to A and P to B is a constant -$$\frac {1}{2}$$.  
(1) Find the equation of the trajectory C of the moving point P;  
(2) Suppose the line l: y=kx+1 intersects the curve C at points M and N. When |MN|= $$\frac {4 \sqrt {2}}{3}$$, find the equation of the line l.

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