
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 Cartesian coordinate system with origin O, let A be the point (6, 2) and B be the point (4, 4). Circle C is the circumcircle of the triangle OAB.
   (1) Find the equation of circle C.
   (2) If a line passing through the point (2, 6) intersects circle C at a chord of length 4, find the equation of the line.

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