
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 $x$ is inversely proportional to $y$. Let $x_1, x_2$ be two nonzero values of $x$ such that $\frac{x_1}{x_2} = \frac{4}{5}$. Let the corresponding $y$ values be $y_1, y_2$. If $y_1, y_2$ are nonzero, find the value of $\frac{y_1}{y_2}$.

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