
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  $\operatorname{cif}(x)$  denote the sum of the digits of the number  $x$  in the decimal system. Put  $a_1=1997^{1996^{1997}}$ , and  $a_{n+1}=\operatorname{cif}(a_n)$  for every  $n>0$ . Find  $\lim_{n\to\infty}a_n$ .

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