
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
Let the function \( g \) be defined such that its domain and range covers all integers, and it is invertible. The following values of \( g \) are given: 
$$\begin{array}{c || c | c | c | c | c}
x & -1 & 0 & 1 & 2 & 3 \\
\hline
g(x) & 3 & 1 & 5 & 7 & 2
\end{array}$$
Determine the value of \( g(g(1)) + g(g^{-1}(3)) + g^{-1}(g^{-1}(7)) \). If there is not enough information to answer this question, enter "NEI".

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