
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 the center C of circle C is on the line y=x and tangent to the positive semi-axis of the x-axis, and the distance between point C and the origin O is $\sqrt {2}$.
(I) Find the standard equation of circle C;
(II) Line l passes through point M(1, $\frac {1}{2}$) and intersects circle C at points A and B. Find the minimum value of chord length |AB| and the equation of line l at this time.

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