
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 functions \( f \) defined on the set of positive real numbers that take positive real values, and satisfy the following conditions:
(1) For all positive numbers \( x \) and \( y \), \( f(x f(y)) = y f(x) \);
(2) As \( x \rightarrow \infty \), \( f(x) \rightarrow 0 \).

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