
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 have radii of 15 units and 25 units, respectively, creating a shaded region between them. A third circle will be drawn such that its area is equal to the area of the shaded region. What must the radius of this third circle be? Express the answer in simplest radical form.

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