
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 a function $f(x)=\left\{\begin{array}{l}(a-2)x, x\geq 2\\-\frac{1}{8}x-\frac{1}{2}, x<2\end{array}\right.$, it satisfies $\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}<0$ for any real numbers $x_{1}\neq x_{2}$. Find the possible range of real number $a$.

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