
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 functions $f(x)=2^{ax}-2$, $g(x)=a(x-2a)(x+2-a)$, where $a\in R$ and $a\neq 0$.
(I) If $\{x|f(x)g(x)=0\}=\{1,2\}$, find the value of the real number $a$.
(II) If $\{x|f(x) < 0 \text{ or } g(x) < 0\}=R$, find the range of the real number $a$.

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