
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$) with one of its vertices at A(2,0) and an eccentricity of $$\frac { \sqrt {2}}{2}$$, the line l passing through point G(1,0) intersects the ellipse C at two distinct points M and N.
1. Find the equation of the ellipse C;
2. When the area of triangle ΔAMN is $$\frac {4 \sqrt {2}}{5}$$, find the equation of the line l.

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