
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 \( f: \mathbb{R} \longrightarrow \mathbb{R} \) such that for any \( x, y \in \mathbb{R} \),
\[ 
(x - y) f(x + y) - (x + y) f(x - y) = 4xy(x^2 - y^2). 
\]

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