
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 eccentricity $$\frac { \sqrt {2}}{2}$$, its left and right foci are F<sub>1</sub> and F<sub>2</sub>, respectively. A line passing through point F<sub>1</sub> intersects the ellipse C at points E and G, and the perimeter of △EGF<sub>2</sub> is 4$$\sqrt {2}$$  
(Ⅰ) Find the equation of ellipse C;  
(Ⅱ) If a line passing through point M(2, 0) intersects the ellipse C at points A and B, and let P be a point on the ellipse such that $$\overrightarrow {OA}+ \overrightarrow {OB}=t \overrightarrow {OP}$$ (O is the origin), when $$| \overrightarrow {PA}- \overrightarrow {PB}| < \frac {2 \sqrt {5}}{3}$$, find the range of the real number t.

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