
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 eccentricity $e= \frac { \sqrt {6}}{6}$ and focal distance of 2, where O is the origin of the coordinate system.  
(1) Find the standard equation of ellipse C;  
(2) The line $y=x+m$ intersects ellipse C at points A and B. If the circle with AB as its diameter passes through point O, find the value of the real number $m$.

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