
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 of the unique circle that passes through the points $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ where $x_k$ and $y_k$ are real parts and imaginary parts of the roots of the equation \[(z-2)(z^2 - 3z + 5)(z^2 - 5z + 10) = 0.\]

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