
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
The price of an item was increased by $q\%$ and subsequently reduced by $r\%$. If the final price of the item was two dollars, the original price was:
**A)** $\frac{20000}{10000 + 100q - r}$  
**B)** $\frac{20000}{10000 + 100(q - r) - qr}$  
**C)** $\frac{20000}{10000 - 100(q + r) + qr}$  
**D)** $\frac{10000}{10000 + 100(q - r) - qr}$

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