
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 \( Q^{+} \) be the set of positive rational numbers. Provide an example of a function \( f: Q^{+} \rightarrow Q^{+} \) such that 

\[ f(x \cdot f(y)) = \frac{f(x)}{y} \]

holds for all \( x, y \in Q^{+} \).

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