
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  $f,g,h: \mathbb{R} \mapsto \mathbb{R}$  such that  $f(x) - g(y) = (x-y) \cdot h(x+y)$  for  $x,y \in \mathbb{R}.$ 

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