
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 the ellipse M: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a > b > 0)$$, the distance from one endpoint of the minor axis to the right focus is 2, and the point A($$\sqrt{2}$$, 1) lies on the ellipse M. The slope of line l is $$\frac{\sqrt{2}}{2}$$, and it intersects ellipse M at points B and C.
(Ⅰ) Find the equation of ellipse M;
(Ⅱ) Determine the maximum area of triangle ABC.

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