
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 statements:

1. The negation of the proposition "$\forall x \in \mathbb{R}, 2x \leq 3$" is "$\exists x \in \mathbb{R}$ such that $2^x > 3$".

2. The function $f(x) = (m^2 - m - 1)x^m$ is a power function, and it is increasing on $x \in (0, +\infty)$, then $m = 2$;

3. The proposition "If the function $f(x)$ has an extremum at $x = x_0$, then $f'(x_0) = 0$" has a true contrapositive;

4. The function $y = \tan\left(2x + \frac{\pi}{6}\right)$ is increasing in the interval $\left(-\frac{\pi}{3}, \frac{\pi}{12}\right)$;

5. "$\log_2(x) > \log_3(x)$" is a necessary and sufficient condition for "$2^x > 3^x$" to hold.

The correct statement numbers are ______.

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