
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 \( n \) be a natural number, and \( f(n) \) be the sum of the digits of \( n^2 + 1 \) (in decimal). Define \( f_1(n) = f(n) \) and \( f_{k+1}(n) = f(f_k(n)) \). Find the value of \( f_{100}(1990) \).

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