
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 $f(x)=\begin{cases} (a-2)x, & x\geqslant 2, \\ \left( \dfrac{1}{2}\right)^{x}-1, & x < 2 \end{cases}$ satisfies that for any real numbers $x_{1}\neq x_{2}$, the inequality $\dfrac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0$ holds, determine the range of the real number $a$.

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