
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
If the point $(4,8)$ is on the graph of $y=g(x)$, and $h(x) = (g(x))^2 + 1$ for all $x$, then there is one point that must be on the graph of $y=h(x)$. What is the sum of the coordinates of that point?

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