
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
Suppose we have two variables $x$ and $z$ such that $z = x^2$. Also, $z$ and another variable $y$ are inversely proportional. If $x$ increases by $p\%$, determine by what percentage $y$ changes.
**A)** $\left(1 - \frac{1}{(1 + 0.01p)^2}\right) \times 100\%$
**B)** $\frac{100p}{100+p}\%$
**C)** $\frac{p}{100+p}\%$
**D)** $\frac{p^2}{(100+p)^2}\%$
**E)** $\left(1 - \frac{1}{1.01p}\right) \times 100\%$

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