
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
Consider a function $g(x)$ such that its values are described in the table below:
\[
\begin{tabular}{|c||c|c|c|c|c|} \hline
$x$ & 1 & 2 & 3 & 4 & 5 \\ \hline
$g(x)$ & 4 & 5 & 1 & 2 & 3 \\ \hline
\end{tabular}
\]
If the inverse $g^{-1}$ of $g$ exists, what is $g^{-1}(g^{-1}(g^{-1}(5)))$?

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