
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 the function $f(n)$ denotes the sum of the digits of $n^2+1$ (where $n\in \mathbb{N}^*$), for example, $14^2+1=197$, and $1+9+7=17$, then $f(14)=17$. Let $f_1(n)=f(n)$, $f_2(n)=f[f_1(n)]$, ..., $f_{k+1}(n)=f[f_k(n)]$ where $k\in \mathbb{N}^*$, what is $f_{2009}(17)$?

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