
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 $f(n)$ be the sum of the digits of $n^2 + 1$ for all $n \in \mathbb{N}^*$. For example, $14^2 + 1 = 197$, $1 + 9 + 7 = 17$, thus $f(14) = 17$. Denote $f\_1(n) = f(n)$, $f\_2(n) = f(f\_1(n))$, $f\_3(n) = f(f\_2(n))$, ... , $f\_{k+1}(n) = f(f\_k(n))$ for $k \in \mathbb{N}^*$. Find $f\_{2017}(9)$.

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