
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 Q ($$\frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{2}$$), the product of the slopes of the lines connecting the moving point P on the ellipse to the two endpoints of the minor axis is $$-\frac{1}{2}$$.

1. Find the equation of the ellipse E.
2. Let $$F_1$$ and $$F_2$$ be the left and right focal points of E, respectively. A line l passes through point $$F_1$$ and intersects E at points A and B. When $$\overrightarrow{F_2A} \cdot \overrightarrow{F_2B} = 2$$, find the area of triangle $$ABF_2$$.

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