
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 units and 34 units respectively. These circles form a shaded region between them. A new circle is to be created whose area equals that of this shaded region. Determine the radius of this new circle and express it in simplest radical form.

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