
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 a circle C that passes through points A(1, 3) and B(5, 1), and the center of the circle C lies on the line $x-y+1=0$.
(1) Find the equation of circle C;
(2) Suppose a line l passes through the point (0, 3), and l is tangent to circle C, find the equation of line l.

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