
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 12 and 25 units, respectively. The region between them is shaded. A third circle is to be drawn such that its area is equal to the shaded region. Determine the radius of this third circle, expressed in simplest radical form.

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