
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
Answer the following questions:<br/>$(1)$ Calculate:<br/>①$\left(x+2\right)\left(x+3\right)=$______；<br/>②$\left(x+2\right)\left(x-3\right)=\_\_\_\_\_\_.$<br/>③$\left(x-2\right)\left(x+3\right)=$______；<br/>④$\left(x-2\right)\left(x-3\right)=\_\_\_\_\_\_.$<br/>$(2)$ Summarize the formula $\left(x+a\right)\left(x+b\right)=x^{2}+\_\_\_\_\_\_x+ab$<br/>$(3)$ Given that $a$,$b$,$m$ are all integers, and $\left(x+a\right)\left(x+b\right)=x^{2}+mx+5$. Find all possible values of $m$.

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