
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 of circle C is at the coordinates (1, 1) and the chord formed by the line l: x + y = 1 on circle C has a length of $\sqrt {2}$,
(I) Find the equation of circle C;
(II) From a point P outside the circle C at (2, 3), draw a tangent line to the circle and find the equation of the tangent line.

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