
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 left and right foci $F_1$ and $F_2$ respectively, an eccentricity of $$\frac { \sqrt {2}}{2}$$, and the line l: y=2x intersecting the ellipse at points M and N. The quadrilateral $MF_1NF_2$ has an area of $$\frac {4 \sqrt {2}}{3}$$.

(I) Find the equation of the ellipse C.
(II) Consider a line parallel to l intersecting the ellipse at points A and B, with P as the midpoint of AB. If the slopes of $PF_1$ and $PF_2$ are $k_1$ and $k_2$ respectively, find the range of values for $k_1 + k_2$.

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