
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
A circle P passes through points A(1,0) and B(4,0).
(1) If circle P also passes through point C(6,-2), find the equation of circle P.
(2) If the ordinate (y-coordinate) of the center P is 2, find the equation of circle P.

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