
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 $n^2 - 2n + 2$ (where $n \in \mathbb{N}^+$), for example, $14^2 - 2 \times 14 + 2 = 170$, and $1 + 7 + 0 = 8$, so $f(14) = 8$. Let $f_1(n) = f(n)$, $f_2(n) = f(f_1(n))$, ..., $f_{k+1}(n) = f(f_k(n))$ (where $k \in \mathbb{N}^+$), then $f_{2010}(17) = \boxed{8}$.

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