
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
Read the following material and complete the answer process.  
Question: In the system of linear equations about $x$ and $y$, $\left\{\begin{array}{l}{x-y=2}\\{x+y=a}\end{array}\right.$, where $x \gt -1$, $y \lt 0$, find the range of values for $a$.  
Analysis: In the system of linear equations about $x$ and $y$, express $x$ and $y$ in terms of the parameter $a$, then write down the inequalities about the parameter $a$ based on $x \gt -1$ and $y \lt 0$ to determine the range of values for $a$.  
Solution: Solve $\left\{\begin{array}{l}{x-y=2}\\{x+y=a}\end{array}\right.$ to get $\left\{\begin{array}{l}{x=\frac{a+2}{2}}\\{y=\frac{a-2}{2}}\end{array}\right.$, and since $x \gt -1$, $y \lt 0$, we have $\left\{\begin{array}{l}{\frac{a+2}{2} \gt -1①}\\{\frac{a-2}{2} \lt 0②}\end{array}\right.$, which leads to ______.  
$(2)$ Please follow the above method to complete the following questions:  
① Given $x-2y=4$, and $x \gt 8$, $y \lt 4$, find the range of values for $3x+2y$.  
② Given $a-b=m$, in the system of linear equations about $x$ and $y$, $\left\{\begin{array}{l}{2x-y=-1}\\{x+2y=5a-8}\end{array}\right.$, where $x \lt 0$, $y \gt 0$, simplify the expression containing absolute values $2|a+b-3+m|+3|m-4+a+b|$ (express the result in terms of $a$).

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