
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 four statements:
① The negation of the proposition "There exists $x \in \mathbb{R}$, such that $x^2+1>3x$" is "For all $x \in \mathbb{R}$, $x^2+1 \leq 3x$";
② "$m=-2$" is a necessary but not sufficient condition for "The line $(m+2)x+my+1=0$ is perpendicular to the line $(m-2)x+(m+2)y-3=0$";
③ When a die is rolled twice, and the numbers appearing are $b$ and $c$ respectively, then the probability that the equation $x^2+bx+c=0$ has real roots is $\frac{19}{36}$;
④ The equation of the line passing through the point $\left(\frac{1}{2}, 1\right)$ and tangent to the graph of the function $y=\frac{1}{x}$ is $4x+y-3=0$.
The correct statement(s) is/are \_\_\_\_\_\_\_\_\_\_\_\_.

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