
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
Observing the factorization carried out by two students, A and B, in the "Exploratory Learning" group:<br/>A: $x^{2}-xy+4x-4y$<br/>$=(x^{2}-xy)+\left(4x-4y\right)$ (split into two groups)<br/>$=x\left(x-y\right)+4\left(x-y\right)$ (directly factor out the common factor)<br/>$=\left(x-y\right)\left(x+4\right)$.<br/>B: $a^{2}-b^{2}-c^{2}+2bc$<br/>$=a^{2}-(b^{2}+c^{2}-2bc)$ (split into two groups)<br/>$=a^{2}-\left(b-c\right)^{2}$ (directly apply the formula)<br/>$=\left(a+b-c\right)\left(a-b+c\right)$ (further apply the difference of squares formula)<br/>Under the inspiration of their solutions, please factorize the following expressions:<br/>$(1)m^{3}-2m^{2}-4m+8$.<br/>$(2)x^{2}-2xy+y^{2}-9$.

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