
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:<br/>In factorization, by treating certain parts of a polynomial as a whole and replacing them with a new letter (i.e. substitution), not only can the structure of the polynomial to be factored be simplified, but also the characteristics of the expression can be made more obvious, making it easier to observe how to factorize. We call this method of factorization "substitution method."<br/>Below is the process of Little Hu using the substitution method to factorize the polynomial $(x^{2}-2x-1)(x^{2}-2x+3)+4$.<br/>Solution: Let $x^{2}-2x=y$,<br/>Original expression $=\left(y-1\right)\left(y+3\right)+4(Step 1)$<br/>$=y^{2}+2y+1(Step 2)$<br/>$=\left(y+1\right)^{2}$(Step 3)<br/>$=(x^{2}-2x+1)^{2}$(Step 4)<br/>Based on the above material, answer the following questions:<br/>$(1)$ In Little Hu's solution, the step from Step 2 to Step 3 uses the factorization of ______;<br/>$A$. extracting common factors method<br/>$B$. square difference formula method<br/>$C$. complete square formula method<br/>$(2)$ The teacher said that Little Hu's factorization result is not thorough, please write down the final result of the factorization: ______;<br/>$(3)$ Please use the substitution method to factorize the polynomial $(x^{2}+6x)(x^{2}+6x+18)+81$.

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