
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
Determine the equations of the following circles that satisfy the given conditions: 
(1) The circle with center C(2, -2) that passes through point P(6, 3).
(2) Given points A(-4, -5) and B(6, -1), find the equation of the circle with diameter AB.

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