
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 23 units and 35 units respectively. A fourth circle is to be drawn such that its area is equivalent to the combined area of both these concentric circles. Calculate the radius of the fourth circle. Express your response in simplest radical form.

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