
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
Regarding the function $y=x^{2}-|bx|-3(b$ is a constant), the following conclusions are made:<br/>① Regardless of the value of $b$, the graph of this function is symmetric about the line $x=\frac{|b|}{2}$;<br/>② If the minimum value of the function is $-3$, then $b=0$;<br/>③ If $b=-2$, then when $-2 \lt x \lt 2$, $-4\leqslant y\leqslant -3$;<br/>④ If $b\neq 0$, and the equation $x^{2}-|bx|-3=m$ has two real roots, then $m \gt -3$ or $b^{2}=-4m-12$.<br/>The correct conclusions are ______. (Fill in the numbers).

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