
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
Given the function $f(x) = e^{1-x}(2ax - a^2)$ where $a \neq 0$.  
(i) If the function $f(x)$ is monotonically decreasing on $(2, +\infty)$, find the range of the real number $a$.  
(ii) Let the maximum value of the function $f(x)$ be $g(a)$, when $a > 0$, find the maximum value of $g(a)$.

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