
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
Find all monotonic positive functions  $f(x)$  defined on the positive reals such that  $f(xy) f\left( \frac{f(y)}{x}\right) = 1$  for all  $x, y$ .	

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