
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
Points \( A(1, 3) \) and \( B(5, 8) \) are the endpoints of a diameter of a circle graphed in a coordinate plane. After translating the circle by the vector \( \mathbf{u} = (2, -1) \), what is the equation of the new circle?

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