
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 vertex of the parabola of the quadratic function $f(x)$ is $A(1, 16)$, and the length of the line segment that the graph cuts on the x-axis is 8.
(1) Find the explicit formula of the function $f(x)$;
(2) Let $g(x) = f(x) + (2a-2)x$, find the maximum value of the function $g(x)$ when $x \in [0, 2]$.

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