
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
An equilateral triangle with side length 10 cm has a circle inscribed in it. A square is then inscribed inside this circle, and finally, a circle is inscribed inside that square. Find the ratio of the area of the innermost circle to the area of the equilateral triangle.

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