
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
For a point M($$\sqrt{6}$$, $$\sqrt{2}$$) lying on the ellipse G: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ (where a > b > 0), with the eccentricity of the ellipse being $$\frac{\sqrt{6}}{3}$$:
(1) Find the equation of ellipse G;
(2) If a line l with slope 1 intersects the ellipse G at points A and B, and an isosceles triangle is constructed with AB as its base and vertex P(-3, 2), find the area of $$\triangle PAB$$.

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