
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
Two circles are placed outside a square $ABCD$, both tangent to its diagonals and one side. The first circle is tangent to side $AB$ and diagonal $AC$, while the second circle is tangent to side $CD$ and diagonal $BD$. Assuming the side length of the square is 1, find the ratio of the area of the second circle to that of the first circle.
A) 0.5
B) 1
C) 2
D) 3

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