
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}{|r||c|c|c|c|c|c|}
\hline
\( x \) & 1 & 2 & 3 & 5 & 8 & 13 \\
\hline
\( g(x) \) & 4 & 12 & 7 & 2 & 1 & 6 \\
\hline
\end{tabular}
\]
If \( g^{-1} \) exists, what is \( g^{-1}\left(\frac{g^{-1}(6) + g^{-1}(12)}{g^{-1}(2)}\right) \)?

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