
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 vertex of the parabola $y=ax^{2}+bx+c$ is $D(-1,4)$, and one intersection point $A$ with the $x$-axis is between the points $(3,0)$ and $(2,0)$ (excluding the endpoints). The correct conclusions are: ①$abc \lt 0$; ②$b=2a$; ③$-4 \lt a \lt -1$; ④$ac+2b \gt 1$. The correct conclusions are ____. (Fill in the numbers)

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