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

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