
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]


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Read the following material and answer the questions.  
$(1)$ Quadratic trinomials of the form $x^{2}+\left(p+q\right)x+pq$ have the following characteristics: ① The coefficient of the quadratic term is $1$; ② The constant term is the product of two numbers; ③ The coefficient of the linear term is the sum of the two factors of the constant term.  
To factorize this quadratic trinomial, we can do it as follows:  
$x^{2}+\left(p+q\right)x+pq$  
$=x^{2}+px+qx+pq$  
$=(x^{2}+px)+\left(qx+pq\right)$  
$=x\left(x+p\right)+q\left(x+p\right)$  
$=\left(x+p\right)\left(x+q\right)$.  
Therefore, we can get $x^{2}+\left(p+q\right)x+pq=\_\_\_\_\_\_.$  
Using the above conclusion, we can directly factorize some quadratic trinomials with a coefficient of $1$ for the quadratic term;  
$(2)$ Using the conclusion in $(1)$, factorize:  
① $m^{2}+7m-18=$______;  
② $x^{2}-2x-8=$______;  
③ $x^{2}y^{2}-7xy+10=\_\_\_\_\_\_$.

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