
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 the ellipse E: $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a>b>0) with left and right foci $F_1$ and $F_2$, respectively, an eccentricity of $$\frac { \sqrt {2}}{2}$$, and $|F_1F_2|=2$.

1. Find the equation of ellipse E.
2. Let B be the lower vertex of the ellipse, and draw a line l passing through the right focus $F_2$ that is symmetric to line $BF_2$ about the x-axis. If line l intersects the ellipse at points M and N, and O is the coordinate origin, find the area of △OMN.

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