
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 $g(x)$ are given in the table below.

\begin{tabular}{|c||c|c|c|c|c|} \hline $x$ & 1 & 2 & 3 & 4 & 5 \\ \hline $g(x)$ & 4 & 3 & 2 & 5 & 1 \\ \hline
\end{tabular}
If $g^{-1}$ exists, then what is $g^{-1}(g^{-1}(g^{-1}(3)))$?

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