
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 circle's radius is increased by 50% of its original radius. Calculate the ratio of the new circumference to the new area. Let the original radius be $r_0$.
**A)** $\frac{2}{r_0}$ **B)** $\frac{4}{3r_0}$ **C)** $\frac{3}{2r_0}$ **D)** $\frac{5}{2r_0}$

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