
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
Two concentric circles with radii of 15 and 25 units bound a shaded region. A third circle is to be drawn with the same area as that of the shaded region. Determine the radius of the third circle. Express your answer in simplest radical form.

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