
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
Cookie Monster now encounters a cookie shaped region defined by the intersection of a circle and an ellipse. The circle is given by the equation $(x-2)^2 + (y-1)^2 = 16$, and the ellipse is given by the equation $\frac{(x-2)^2}{25} + \frac{(y-1)^2}{9} = 1$. Determine the radius of the circle.

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