
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 \( f \) whose domain consists of all positive real numbers and whose values are positive real numbers, satisfying the following conditions: 
1. \( f[x f(y)] = y f(x) \) for all \( x, y \in \mathbf{R}^{+} \).
2. As \( x \rightarrow \infty \), \( f(x) \rightarrow 0 \).

(IMO - Problem 24)

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