
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 an invertible function $g$ with real numbers as both domain and range values given by:
$$\begin{array}{c || c | c | c | c | c}
x & 1 & 2 & 3 & 4 & 5 \\
\hline
g(x) & 3 & 4 & 6 & 8 & 9
\end{array}$$
Calculate the value of $g(g(3)) + g(g^{-1}(3)) + g^{-1}(g^{-1}(6))$. If there is not enough information, indicate by "NEI".

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