
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 E: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}$$\=1 (a>b>0) passing through point P ($$\sqrt {3}$$, $$\frac {1}{2}$$) with its left focus at F ($$-\sqrt {3}$$, 0).

1. Find the equation of ellipse E.
2. If A is the right vertex of ellipse E, and the line passing through point F with a slope of $$\frac {1}{2}$$ intersects ellipse E at points M and N, find the area of △AMN.

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