
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
The values of a function $f(x)$ are given in the table below.

\[
\begin{array}{|c||c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
f(x) & 4 & 6 & 2 & 5 & 3 & 1 \\
\hline
\end{array}
\]
If $f^{-1}$ exists, then what is $f^{-1}(f^{-1}(f^{-1}(4)))$?

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