
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 inequality $mx-3 \gt 2x+m$.  
$(1)$ If its solution set is $x \lt \frac{m+3}{m-2}$, find the range of $m$;  
$(2)$ If its solution set is the same as the solution set of the inequality $2x-1 \gt 3-x$, find the value of $m$.

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