
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
Given three positive numbers \( p \), \( q \), and \( M \) such that \( q < p \), the number derived by first increasing \( M \) by \( p\% \) and then increasing the result by \( q\% \) exceeds \( M \) if and only if which of the following is true?
**A)** \( p > q \) \\
**B)** \( p > \frac{100q}{100 + q} \) \\
**C)** \( p > 0 \) and \( q > 0 \) \\
**D)** \( p > \frac{100 + q}{100 - p} \) \\
**E)** \( p > \frac{q}{1 - q} \)

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