
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
If $f(n)$ is the sum of the digits of $n^2 + 1$ ($n \in N^*$), for example, $14^2 + 1 = 197$, and $1 + 9 + 7 = 17$, then $f(14) = 17$. Let $f_1(n) = f(n)$, $f_2(n) = f(f_1(n))$, ..., $f_{k+1}(n) = f(f_k(n))$ ($k \in N^*$), then $f_{2017}(9) = \boxed{\phantom{4}}$.

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