
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 square is inscribed in a circle, and then a circle is inscribed in this square. Finally, a square is inscribed in the second circle. What is the ratio of the area of the second circle to the area of the original circle?

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