
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 pairs  $(f,h)$  of functions  $f,h:\mathbb{R}\rightarrow\mathbb{R}$  such as for all real  $x$  and  $y$  the equation holds.   $$ f(x^2+yh(x))=xh(x)+f(xy) $$  

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