
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
Given the following five propositions:

1. If the equation $x^{2}+(a-3)x+a=0$ has one positive real root and one negative real root, then $a < 0$;
2. The function $y= \sqrt {x^{2}-1}+ \sqrt {1-x^{2}}$ is an even function, but not an odd function;
3. If the range of the function $f(x)$ is $[-2,2]$, then the range of the function $f(x+1)$ is $[-3,1]$;
4. If the domain of the function $y=f(x)$ is $R$, then the graphs of the functions $y=f(1-x)$ and $y=f(x-1)$ are symmetric about the $y$-axis;
5. The number of common points $m$ between the curve $y= \begin{cases} 3-x^{2}(x\in\[- \sqrt {3}, \sqrt {3}\]) \\ x^{2}-3(x\in(-∞,- \sqrt {3})∪( \sqrt {3},+∞))\end{cases}$ and the line $y=a(a\in R)$ cannot be $1$.

Write out the serial numbers of all correct propositions.

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