
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  $f: N_0 \to N_0$ , (where  $N_0$  is the set of all non-negative integers) such that  $f(f(n))=f(n)+1$  for all  $n \in N_0$  and the minimum of the set  $\{ f(0), f(1), f(2) \cdots \}$  is  $1$ .

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