
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: Factorization: $\left(x+y\right)^{2}+2\left(x+y\right)+1$.  
Solution: Consider "$x+y$" as a whole, let $x+y=A$, then the original expression $=A^{2}+2A+1=\left(A+1\right)^{2}$. Then restore "$A$", we get the original expression $=\left(x+y+1\right)^{2}$. The above solution uses the "whole concept," which is a commonly used method in mathematical problem solving. Please use the "whole concept" to solve the following problems:  
$(1)$ Factorization: $\left(x-y\right)^{2}-2\left(x-y\right)+1$;  
$(2)$ Factorization: $\left(a+b\right)\left(a+b-4\right)+4$;  
$(3)$ Calculate: $\left(a+4b-3c\right)\left(a-4b-3c\right)$.

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