
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
A circle is inscribed in a rectangle with a length twice its width. Inside this circle, a square is inscribed. Finally, a circle is inscribed inside this square. What is the ratio of the area of the smaller innermost circle to the area of the original rectangle?

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