
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 $$A(- \sqrt {3}, 0)$$, and B is a moving point on the circle $$C: (x- \sqrt {3})^{2}+y^{2}=16$$ (with C as the center), the perpendicular bisector of AB intersects BC at point E.  
(1) Find the equation of the trajectory of the moving point E;  
(2) Suppose the line $$l: y=kx+m$$ ($$k \neq 0, m > 0$$) intersects the trajectory of E at points P and Q, and one vertex of the rhombus with PQ as its diagonal is $(-1, 0)$. Find the maximum area of $$\triangle OPQ$$ and the equation of line l at this time.

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