
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 first, then answer the following questions:<br/>Material: Factorization: $\left(x+y\right)^{2}+2\left(x+y\right)+1$.<br/>Solution: Regard "$x+y$" as a whole, let $x+y=m$, then the original expression $=m^{2}+2m+1=\left(m+1\right)^{2}$.<br/>Substitute $x+y=m$ back in, we get the original expression $=\left(x+y+1\right)^{2}$.<br/>The above solution uses the "whole concept," which is a commonly used method in mathematical problem-solving. Please write down the results of the following factorizations:<br/>$(1)$ Factorization: $1-2\left(x-y\right)+\left(x-y\right)^{2}=$______;<br/>$(2)$ Factorization: $25\left(a-1\right)^{2}-10\left(a-1\right)+1=$______;<br/>$(3)$ Factorization: $(y^{2}-4y)(y^{2}-4y+8)+16=\_\_\_\_\_\_$.

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