
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. Then, a circle is inscribed in this square, and finally, a square is inscribed in this smaller circle. What is the ratio of the area of the final square to the area of the initial circle?

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