
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ passing through point P(2,0), with an eccentricity of $$\frac { \sqrt {2}}{2}$$, and a line l: y=x+m intersecting the ellipse at points A and B.
(1) Find the equation of the ellipse;
(2) If there exists a point Q on the y-axis such that △QAB is a right triangle, find the value of m.

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