
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 wire is cut into two pieces, one of length \(a\) and the other of length \(b\). The first piece \(a\) is bent to form a rectangle where the length is twice the width. The second piece \(b\) is bent to form a circle. Both the rectangle and the circle have equal areas. What is \(\frac{a}{b}\)?

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