
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 $\mathbf{R}^{+}$ be the set of all positive real numbers. Find all functions \( f: \mathbf{R}^{+} \rightarrow \mathbf{R}^{+} \) such that \( f(x) + f(y) = f(x y f(x+y)) \) for all \( x, y \in \mathbf{R}^{+} \) where \( x + y \neq 0 \).

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