
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 F1(-c, 0) and F2(c, 0) are the left and right foci of the ellipse G: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where \(0 < b < a < 3\), and P(2, $$\sqrt{2}$$) lies on the ellipse G. Also, \(|PF_1| - |PF_2| = a\).
1. Find the equation of the ellipse G.
2. Let line l intersect the ellipse G at points A and B. If $$\vec{OA} \perp \vec{OB}$$ where O is the origin, determine whether the distance from O to line l is constant. If yes, find the constant distance; if no, explain why.

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