
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
Let there's a function  $ f: \mathbb{R}\rightarrow\mathbb{R}$  
Find all functions  $ f$  that satisfies:
a)  $ f(2u)\equal{}f(u\plus{}v)f(v\minus{}u)\plus{}f(u\minus{}v)f(\minus{}u\minus{}v)$ 
b)  $ f(u)\geq0$ 

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