
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
Determine the correct statement(s) from the following four options:

1. The negation of the proposition "For all $x \in \mathbb{R}$, $x^2 - 2 < 3x$" is "There exists an $x \in \mathbb{R}$ such that $x^2 - 2 \geq 3x$."
2. If $a, b \in \mathbb{R}$, then $2^a < 2^b$ is a necessary but not sufficient condition for $\log_{\frac{1}{2}} a > \log_{\frac{1}{2}} b$.
3. By moving all points on the graph of the function $y = \sin(-3x) (x \in \mathbb{R})$ to the right by $\frac{\pi}{4}$ units, the graph of $y = \sin(-3x - \frac{\pi}{4}) (x \in \mathbb{R})$ can be obtained.
4. If vectors $\vec{a}$ and $\vec{b}$ satisfy $|\vec{a}| = 1$, $|\vec{b}| = 2$, and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{2\pi}{3}$, then $|\vec{a} + \vec{b}| = \sqrt{3}$.

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