
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 squares of the digits of the positive integer $n$ (in decimal notation). Define $f_1(n) = f(n)$, and $f_{k+1}(n) = f[f_k(n)]$ (where $k=1,2,3,\ldots$). Compute $f_{2007}(2007)$.

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