
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 $f(x)=\left\{\begin{array}{l}{a^x}(x>1)\\(4-\frac{a}{2})x+2(x\leq 1)\end{array}\right.$ satisfies $\frac{{f({x_1})-f({x_2})}}{{{x_1}-{x_2}}} > 0$ for any $x_{1} \neq x_{2}$ in $R$, then the range of real number $a$ is ____.

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