
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 25 units and 40 units. A third circle is to be drawn such that its area is half the area of the region between the two original circles. 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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