
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 the number of functions  $ f: \mathbb N\rightarrow\mathbb N$  which satisfying:
(i)  $ f(1) \equal{} 1$ 
(ii)  $ f(n)f(n \plus{} 2) \equal{} f^2(n \plus{} 1) \plus{} 1997$  for every natural numbers n.

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