
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
Given the irrational number $\mathrm{e} = 2.71828182845 \cdots$, define the function $f(n) = k$, where the domain is the set of positive integers, and $k$ is the $n$-th digit after the decimal point of $\mathrm{e}$. Given $f(0) = 2$, determine the range of $f(f(f(n)))$.

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