
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
In a diagram, a smaller circle is inscribed within a larger circle. The gray area exposed around the smaller circle within the larger circle is equal to five times the area of the white circular region of the smaller circle. Determine the ratio of the radius of the small circle to the radius of the large circle.

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