
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
If $\alpha$, $\beta$, $p$, and $q$ are positive numbers, and $q<50$, then the number obtained by increasing $\alpha \times \beta$ by $p\%$ followed by a decrease by $q\%$ exceeds $\alpha \times \beta$ if and only if...
A) $p > q$  
B) $p > \dfrac{q}{100-q}$  
C) $p > \dfrac{q}{1-q}$  
D) $p > \dfrac{100q}{100+q}$  
E) $p > \dfrac{100q}{100-q}$

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