
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\mathbb{R}$  satisfying following conditions.
(a)  $ f(x) \ge 0 $  for all  $ x \in \mathbb{R} $ .
(b) For  $ a, b, c, d \in \mathbb{R} $  with  $ ab + bc + cd = 0 $ , equality  $ f(a-b) + f(c-d) = f(a) + f(b+c) + f(d) $  holds.

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