
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 with center C that passes through points A(0, -6) and B(1, -5), and the center of the circle lies on the line $l: x-y+1=0$.
(1) Find the standard equation of the circle with center C;
(2) Draw a tangent line to the circle passing through point M(2, 8), and find the equation of the tangent line.

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