
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 : Z\rightarrow Z$  for which we have  $ f (0) \equal{} 1$  and  $ f ( f (n)) \equal{} f ( f (n\plus{}2)\plus{}2) \equal{} n$ , for every natural number  $ n$ .

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