
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

Find the radius and the coordinates of the center of the circle given by the following equations:

a) \((x-3)^{2}+(y+2)^{2}=16\)

b) \(x^{2}+y^{2}-2(x-3y)-15=0\)

c) \(x^{2}+y^{2}=x+y+\frac{1}{2}\)

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