
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 square with a side length of 4 units. Subsequently, a square is inscribed within this circle, and then a circle is inscribed within this new square. What is the ratio of the area of the final inscribed circle to the area of the initial larger square?

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