
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  $f : \mathbb{R}\to \mathbb{R}$  , bounded in  $(0,1)$  and satisfying: $x^2 f(x) - y^2 f(y) = (x^2-y^2) f(x+y) -xy f(x-y)$ for all  $x,y \in \mathbb{R}$ *Proposed by Nikolay Nikolov*

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