
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 larger circle, then a circle is inscribed in this square, followed by a square inscribed in this circle, and finally, a circle is inscribed in this last square. What is the ratio of the area of the smallest circle to the area of the largest circle?

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