
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
The parabola $y=ax^{2}+bx+c$ (where $a$, $b$, $c$ are constants) opens upwards and passes through points $A(1,0)$ and $B(m,0)$ ($-2 < m < -1$). The following conclusions are given: ① $abc < 0$; ② $2a+c < 0$; ③ If points $P_{1}(t-1, y_{1})$ and $P_{2}(t+1, y_{2})$ are both on the parabola, when $t > 0$, then $y_{1} < y_{2}$; ④ If the equation $a(x-m)(x-1)+1=0$ has no real roots, then $b^{2}-4ac < 4a$. The correct conclusions are ______.

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