
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: The overall idea is a common thinking method used in mathematical problem solving. Below is a process of a student factorizing the polynomial $(x^{2}-3x+4)(x^{2}-3x+6)+1$. Solution: Let $x^{2}-3x=m$, Original expression $=\left(m+4\right)\left(m+6\right)+1$ (Step 1), $=m^{2}+10m+25$ (Step 2), $=\left(m+5\right)^{2}$ (Step 3), $=(x^{2}-3x+5)^{2}$ (Step 4). Answer the following questions: (1) The method used by the student from the second step to the third step is ______. $A$. Extracting common factors $B$. Difference of squares $C$. Completing the square (2) Please try to factorize the polynomial $(a^{2}-4a+2)(a^{2}-4a+6)+4$ using the above method.

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