
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 quadratic function $y=ax^{2}+bx+c$ (where $a$, $b$, and $c$ are constants) with a downward opening and passing through points $A(1,0)$, $B(m,0)$, $(-2 < m < -1)$. The following conclusions are given: ① $b < 0$, ② $a+b+c=0$, ③ $a(m+1)-b+c > 0$, ④ If the equation $a(x-1)(x-m)-1=0$ has two distinct real roots, then $4ac-b^{2} > 4a$. The correct conclusions are ______ (fill in the corresponding numbers).

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