
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
If the sum of two fractions $P$ and $Q$ is a constant $m$, and $m$ is a positive integer, then $P$ and $Q$ are called "perfect fractions" to each other, and the constant $m$ is called the "perfect value". For example, if the fractions are $P=\frac{x}{x+1}$ and $Q=\frac{1}{x+1}$, then $P+Q=\frac{x+1}{x+1}=1$, so $P$ and $Q$ are "perfect fractions" to each other, and the "perfect value" $m=1$.  
$(1)$ Given fractions $A=\frac{x-1}{x-4}$ and $B=\frac{x-7}{x-4}$, determine whether $A$ and $B$ are "perfect fractions". If not, please explain the reason; if yes, find the "perfect value" $m$.  
$(2)$ Given fractions $C=\frac{3x-4}{x-2}$ and $D=\frac{E}{{x}^{2}-4}$, if $C$ and $D$ are "perfect fractions" and the "perfect value" $m=3$, where $x$ is a positive integer and the value of fraction $D$ is a positive integer.  
① Find the algebraic expression represented by $E$;  
② Find the value of $x.

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