
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 with radii of 17 and 27 units respectively bound a shaded region. If a third circle is drawn such that its area is equal to the area of the shaded region, what must the radius of the third circle be? Express your answer in simplest radical form.

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