
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  $f\colon \mathbb{R}\to\mathbb{R}$  that satisfy   $f(x+y)-f(x-y)=2y(3x^2+y^2)$  for all  $x,y{\in}R$ ______________________________________
Azerbaijan Land of the Fire :lol:

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