
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 $f(x)=\begin{cases} & (a-2)x, & x\geqslant 2, \\ & 2^{x}-1, & x < 2 \end{cases}$, determine the range of values for the real number $a$ for which the function is monotonically increasing over the interval $(-\infty ,+\infty )$.

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