
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  $f,g : N \to N$  such that for all  $m ,n \in  N$  the following relation holds:   $$ f(m ) - f(n) = (m - n)(g(m) + g(n)) $$  . 
Note:  $N = \{0,1,2,...\}$ 

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