
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
For the algebraic expression $ax^{2}+bx+c(a\neq 0$,$a$,$b$,$c$ are constants), ① if $b^{2}-4ac=0$, then the equation $ax^{2}+bx+c=0$ has two equal real roots; ② there exist three distinct real numbers $m\neq n\neq s$, such that $am^{2}+bm+c=an^{2}+bn+c=as^{2}+bs+c$; ③ if $ax^{2}+bx+c+2=0$ has the same solutions as the equation $\left(x+2\right)\left(x-3\right)=0$, then $4a-2b+c=-2$. The correct statements are ______.

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