
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 $f(n)$ represents the sum of the digits of $n^2 + 1$ where $n \in \mathbb{N}^*$, such as $14^2 + 1 = 197$ and the sum of its digits $1+9+7=17$, then $f(14)=17$. Define $f_1(n) = f(n)$, $f_2(n) = f(f_1(n))$, and so on until $f_{k+1}(n) = f(f_k(n))$ where $k \in \mathbb{N}^*$. Find the value of $f_{2008}(8)$.

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