
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 of the equation $m(1-x)=x+3$ is the same as the solution of the equation $2-x=x+4$, find the value of $m$.  
$(2)$ Under the condition of $(1)$, find the solution of the system of equations in terms of $x$ and $y$: $\left\{\begin{array}{l}{3x+2m=-y}\\{2x+2y=m-1}\end{array}\right.$.  
$(3)$ A diligent student, Xiao Yi, found that regardless of the value of $m$, there is a relationship between the solutions $x$ and $y$ of the system of equations in $(2)$. Find this relationship.

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