
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 $f(n) = k$, where $n \in \mathbb{N}$, and $k$ is the digit in the $n$-th position after the decimal point of $\pi = 3.1415926535\ldots$, for example, $f(2) = 4$, then $f\{f\ldots f[f(7)]\}$ (with a total of 2007 $f$'s) equals to.

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