
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 G: $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 (a > b > 0) with its right focus at (2 $$\sqrt {2}$$, 0) and eccentricity of $$\frac { \sqrt {6}}{3}$$. A line l with slope 1 intersects the ellipse G at points A and B.

(I) Find the standard equation of the ellipse.
(II) If the y-intercept of line l is m, find the range of real values for m.
(III) If an isosceles triangle PAB is constructed with AB as its base and P as its apex at (-3, 2), find the area of △PAB.

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