
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
In the rectangular coordinate system xOy, an ellipse C is given by the equation $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ ($$a>b>0$$), with left and right foci $$F_1$$ and $$F_2$$, respectively. The left vertex's coordinates are ($$-\sqrt {2}$$, 0), and point M lies on the ellipse C such that the perimeter of $$\triangle MF_1F_2$$ is $$2\sqrt {2}+2$$.

(1) Find the equation of the ellipse C;
(2) A line l passes through $$F_1$$ and intersects ellipse C at A and B, satisfying |$$\overrightarrow {OA}+2 \overrightarrow {OB}$$|=|$$\overrightarrow {BA}- \overrightarrow {OB}$$|, find the area of $$\triangle ABO$$.

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