
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 an ellipse C with its center of symmetry at the origin O, and its foci on the x-axis, labeled as F<sub>1</sub> and F<sub>2</sub>. Let B and A be the top and right vertices, respectively, and let D be the midpoint of line segment AB. It is given that the product of the slopes of DD and AN is $$\frac {1}{2}$$, and the area of △AOB is $$2 \sqrt {2}$$.  
(1) Determine the equation of the ellipse C.  
(2) A line l passing through F<sub>1</sub> intersects ellipse C at points M and N. If the area of △MF<sub>2</sub>N is $$\frac {16}{3}$$, find the equation of the circle with center F<sub>2</sub> that is tangent to the line l.

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