
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 the function $f(n)$ represent the sum of the digits of $n^2 + 1$ where $n \in \mathbb{N}^*$.  
For example, since $14^2+1 = 197$, the sum of the digits is $1+9+7=17$, so $f(14)=17$.  
Denote $f_1(n) = f(n)$, $f_2(n) = f[f_1(n)]$, ..., $f_{k+1}(n) = f[f_k(n)]$ for $k \in \mathbb{N}^*$.  
Find the value of $f_{2010}(17)$.

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