
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
1. If the line $3x-4y+12=0$ intersects the coordinate axes at points A and B, find the equation of the circle with diameter AB.
2. A circle passes through points A(3,1) and B(-1,3), and its center lies on the line $3x-y-2=0$. Find the equation of the circle.

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