
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 graph intersects the x-axis, creating a segment of length 8.  
(1) Find the expression for the function $f(x)$.  
(2) Let $g(x) = (2-2a)x - f(x)$. If the maximum value of $g(x)$ in the interval $[0, 2]$ is 5, find the value of the real number $a$.

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