
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
Let $S$ be a positive number. Suppose we increase $S$ by $x\%$, add 15, and then decrease the result by $y\%$. Determine when the resulting number exceeds $S$ by at least 10 units. Assume $x > y > 0$.
**A)** \( x = y + \frac{1500}{S} \)  
**B)** \( x > y + \frac{xy}{100} + 500 - \frac{1500y}{S} \)  
**C)** \( x < y - \frac{xy}{100} + 500 + \frac{1500y}{S} \)  
**D)** \( x > 500 + \frac{1500y}{S} \)

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