
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 an ellipse C: $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a＞b＞0) with a focal length of 2, and it passes through the point (1, $$\frac { \sqrt {2}}{2}$$).
(I) Find the equation of the ellipse C;
(II) A line passing through point M(2,0) intersects ellipse C at points A and B. P is a point on the ellipse C, and O is the origin of the coordinate, satisfying $$\overrightarrow {OA}$$+ $$\overrightarrow {OB}$$\=t $$\overrightarrow {OP}$$, where t∈($$\frac {2 \sqrt {6}}{3}$$,2). Find the range of values for |AB|.

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