
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
Define: If a one-variable linear equation about $x$: $ax+b=0 (a\neq 0)$ has a solution of $x=\frac{a+b}{2}$, then this equation is called a "midpoint equation". For example, the solution of the equation $2x-1=0$ is $x=\frac{1}{2}$, and $\frac{1}{2}=\frac{2+(-1)}{2}$, so the equation $2x-1=0$ is a "midpoint equation".<br/>$(1)$ Is the equation $4x-\frac{8}{3}=0$ a "midpoint equation"? Please explain the reason;<br/>$(2)$ If the equation about $x$ is $5x+m-1=0$ a "midpoint equation", find the value of $m$.

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