
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 following propositions:<br/>① The equation $x^{2}+\left(a-3\right)x+a=0$ has one positive real root and one negative real root, then $a \lt 0$;<br/>② The function $y=\sqrt{{x}^{2}-1}+\sqrt{1-{x}^{2}}$ is an even function, but not an odd function;<br/>③ If the range of the function $f\left(x\right)$ is $\left[-2,2\right]$, then the range of the function $f\left(x+1\right)$ is $\left[-3,1\right]$;<br/>④ The number of common points between the curve $y=|3-x^{2}|$ and the line $y=a\left(a\in R\right)$ is $m$, then the value of $m$ cannot be $1$.<br/>Among these, the correct ones are ____.

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