
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 $$e= \frac { \sqrt {2}}{2}$$, and the focal distance is 2  
(1) Find the equation of ellipse C;  
(2) It is known that ellipse C intersects with the line $x-y+m=0$ at two distinct points M and N, and the midpoint of segment MN is not inside the circle $x^{2}+y^{2}=1$, find the range of the real number $m$.

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