
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 14 and 34 units, respectively. The region between them is shaded. A third circle is to be drawn, and its area must equal that of the shaded area between the two concentric circles. Determine the radius of this third circle in simplest radical form.

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