
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 that point O is the coordinate origin, and the left and right foci of the ellipse C: $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 (a > b > 0) are F1 and F2 respectively, |F1F2| = 2. The ellipse passes through the point (-1, $- \frac { \sqrt {2}}{2}$).

1. Find the standard equation of the ellipse C.
2. A line passing through point H(-2, 0) intersects the ellipse C at points A and B. If AF1 is perpendicular to BF1, find the equation of the line AB.

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