
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 $n^2+1$ where $n \in \mathbb{N}^*$. For example, $14^2+1=197$, $1+9+7=17$, thus $f(14)=17$. Denote $f_1(n)=f(n)$, $f_2(n)=f(f_1(n))$, ..., $f_{k+1}(n)=f(f_k(n))$, $k \in \mathbb{N}^*$. Find $f_{2018}(8)= \_\_\_\_\_\_.$

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