
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 an eccentricity of $$\frac { \sqrt {2}}{2}$$, and it passes through point Q（1， $$\frac { \sqrt {2}}{2}$$）.
(1) Find the equation of the ellipse C;
(2) If a line passing through point M（2，0） intersects with ellipse C at points A and B, and point P is on the line x+y-1=0, and $$\overrightarrow {OA}+ \overrightarrow {OB}=t \overrightarrow {OP}$$ (O is the origin of the coordinate), find the minimum value of the real number t.

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