
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 24 and 35 units, defining a shaded region between them. Another circle is to be drawn with an area equal to that of the shaded region. Determine the required radius of this new circle, expressing the answer in simplest radical form.

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