
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 unit circle, then a circle is inscribed in this square, followed by inscribing another square in this circle. This process is repeated indefinitely. Determine the ratio of the total area of all circles to the total area of all squares.

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