
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
Let $y=mx^{2}+\left(1-m\right)x+m-2$.  
$(1)$ If the inequality $y\geqslant -2$ holds for all real numbers $x$, find the range of real number $m$;  
$(2)$ Given $m \lt 0$, solve the inequality $mx^{2}+\left(1-m\right)x+m-2 \lt m-1$.

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