
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 an arrangement, the visible gray area within the larger circle is equal to four times the area of the white circular region as shown in the diagram:
[asy]size(101);
filldraw(Circle((0,0),2)^^Circle((.6,-.2),1),gray(.6)+fillrule(1),black);[/asy]
What is the ratio of the radius of the small circle to the radius of the large circle? Express your answer as a common fraction.

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