
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. If proposition $p$: $\exists x_{0} \in \mathbb{R}$, $\tan x_{0} = 2$; proposition $q$: $\forall x \in \mathbb{R}$, $x^{2} - x + \frac{1}{2} > 0$. Then the proposition "$p \land (\neg q)$" is a false proposition;

2. Given lines $l_{1}$: $ax + 3y - 1 = 0$, $l_{2}$: $x + by + 1 = 0$, then the necessary and sufficient condition for $l_{1} \perp l_{2}$ is $\frac{a}{b} = -3$;

3. "Let $a, b \in \mathbb{R}$, if $ab \geqslant 2$, then $a^{2} + b^{2} > 4$" has the negation: "Let $a, b \in \mathbb{R}$, if $ab < 2$, then $a^{2} + b^{2} \leqslant 4$".

The correct statement(s) is/are __________.

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