
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
Among the following propositions:

1. The contrapositive of the proposition "If $x^{2}-3x+2=0$, then $x=1$ or $x=2$" is "If $x \neq 1$ or $x \neq 2$, then $x^{2}-3x+2 \neq 0$";

2. The negation of the proposition "There exists an $x \in \mathbb{R}$ such that $x^{2}-2x+1 < 0$" is a true proposition;

3. "$m= \frac{1}{2}$" is a sufficient but not necessary condition for "The line $(m+2)x+3my+1=0$ is perpendicular to the line $(m-2)x+(m+2)y-3=0$";

4. For constants $m$, $n$, "The equation $x^{2}-mx+n=0$ has two positive roots" is a sufficient but not necessary condition for "The curve of the equation $\frac{x^{2}}{m}+ \frac{y^{2}}{n}=1$ is an ellipse", the serial numbers of true propositions are.

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