
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 function $f(x)=\left\{{\begin{array}{l}{{a^x},x＞1}\\{({4-\frac{a}{2}})x+2,x≤1}\end{array}}\right.$ satisfies the inequality $(x_{1}-x_{2})[f(x_{1})-f(x_{2})] \gt 0$ for any two distinct real numbers $x_{1}$ and $x_{2}$ in $R$, then the range of real number $a$ is ______.

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