
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 functions $y_1=x^2+ax+b(a,b∈R)$, $y_2=x^2+x-2$.

$(1)$ Find the solution set of the inequality $y_{2} \lt 0$.

$(2)$ If $|y_{1}|\leqslant |y_{2}|$ holds for all $x\in R$, find the values of $a$ and $b$.

$(3)$ Under the condition in $(2)$, if $y_{1} \gt \left(m-2\right)x-m$ holds for all $x \gt 1$, find the range of real number $m$.

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