
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 $y=(m+1)x^{2}-mx+m-1$ where $m\in \mathbb{R}$.  
$(1)$ If the solution set of the inequality $y \lt 0$ is $\varnothing$, find the range of $m$.  
$(2)$ When $m \gt -2$, solve the inequality $y\geqslant m$.

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