
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 C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (a > b > 0) with an eccentricity of $$\frac { \sqrt {2}}{2}$$ and its left focus F (-2, 0).
(I) Find the equation of ellipse C.
(II) If the line y = x + m intersects curve C at distinct points A and B, and the midpoint M of segment AB lies on the curve x^2 + 2y = 2, find the value of m.

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