
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
An ellipse M is given by the equation $$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$ ($$a > b > 0$$) with an eccentricity of $$e = \frac{\sqrt{2}}{2}$$. A line passing through points A($$-a, 0$$) and B($$0, b$$) has a distance of $$\frac{\sqrt{6}}{3}$$ from the origin.

1. Find the equation of the ellipse M.
2. A line l passing through point E($$1, 0$$) intersects ellipse M at points C and D, where point D is located in the first quadrant. When $$\frac{CE}{DE} = 3$$, find the equation of line l.

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