
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 configuration, two concentric circles form two regions: an outer gray region and an inner white region. The area of the gray region within the larger circle is equal to four times the area of the white circular region. What is 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}
user