
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 that circle C is tangent to the positive half-axes of both coordinate axes and the distance from the center C to the line y=-x is equal to $\sqrt {2}$,  
(1) find the equation of circle C;  
(2) if a line $l: \frac {x}{m}+ \frac {y}{n}=1$ (where $m>2, n>2$) is tangent to circle C, find the minimum value of mn.

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