
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 \( f, g, h : \mathbf{R} \rightarrow \mathbf{R} \) that satisfy the equation:
\[ 
f(x) - g(y) = (x - y) h(x + y), \quad \forall x, y \in \mathbf{R}. 
\]

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