
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  $f: \mathbb{R}\to [0;+\infty)$  such that: 
\[f(x^2+y^2)=f(x^2-y^2)+f(2xy)\]
for all real numbers  $x$  and  $y$ .

*Laurentiu Panaitopol*

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