
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 material and solve the problem: Factorize $\left(a+b\right)^{2}+2\left(a+b\right)+1$. Solution: Let $a+b=t$, then the original expression $=t^{2}+2t+1=\left(t+1\right)^{2}=\left(a+b+1\right)^{2$; this solving method is called "substitution method", that is, when a certain term repeats in a complex polynomial, we replace it with a letter to simplify the polynomial. The substitution method is an important mathematical method, and many problems can be solved using it. Please use the "substitution method" to factorize the following polynomials:  
$(1)\left(m+n\right)^{2}-10\left(m+n\right)+25$;  
$(2)(x^{2}-6x+8)(x^{2}-6x+10)+1$.

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