
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
$(1)$ If the solution set of the inequality $mx^{2}+mx+m-6 \lt 0$ with respect to $x$ is non-empty, find the range of real numbers $m$; <br/>$(2)$ If for all $x\in \left[-2,1\right]$, the inequality $mx^{2}-mx \lt -m+2$ always holds, find the range of real numbers $m$.

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