
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: We give the following definition: Given two non-overlapping points $A$ and $B$ on the number line, if there exists a point $M$ on the number line such that the distance from point $M$ to point $A$ is equal to the distance from point $M$ to point $B$, then point $M$ is called the "Yazhong point" of points $A$ and $B". Answer the following questions:  
$(1)$ If the number represented by point $A$ is $-5$, the number represented by point $B$ is $1$, and point $M$ is the "Yazhong point" of points $A$ and $B", then the number represented by point $M$ is ______;  
$(2)$ If the number represented by the "Yazhong point $M$" of points $A$ and $B$ is $2$, the distance between points $A$ and $B$ is $9$ (with $A$ to the left of $B$), then the numbers represented by points $A$ and $B$ are ______ and ______;  
$(3)$ The number represented by point $A$ is $-6$, point $O$ is the origin of the number line, points $C$ and $D$ represent the numbers $-4$ and $-2$ respectively, and $B$ is a point on the line segment (point $B$ can coincide with points $C$ and $D$).  
① Let the number represented by point $M$ be $m$, if point $M$ can be the "Yazhong point" of points $A$ and $B", then the integer values that $m$ can take are ______;  
② If points $C$ and $D$ move the same distance $n$ in the direction of the positive half-axis of the number line, such that point $O$ can be the "Yazhong point" of points $A$ and $B", then all integer values of $n$ are ______.

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