
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  $ S$  be the set of nonnegative integers. Find all functions  $ f,g,h: S\rightarrow S$  such that

 $ f(m\plus{}n)\equal{}g(m)\plus{}h(n),$  for all  $ m,n\in S$ , and

 $ g(1)\equal{}h(1)\equal{}1$ .

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