
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 $x$, $y$, and $z$ be positive numbers such that $x$ and $y$ are inversely proportional, and $z$ is directly proportional to $x$ and inversely to $y$. If $x$ increases by 20%, calculate the percentage decrease in $y$ and then the resulting change in $z$ as a percentage of its original value.

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