
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
There are four propositions as follows:
1. If proposition P: $\forall x \in \mathbb{R}, \sin x \leq 1$, then $\neg P: \forall x \in \mathbb{R}, \sin x > 1$;
2. There exist $\alpha, \beta \in \mathbb{R}$ such that $\sin(\alpha + \beta) = \sin \alpha + \sin \beta$;
3. If $\{a_n\}$ is a geometric sequence; A: $m+n=p+q$ ($m, n, p, q \in \mathbb{N}^*$)    B: $a_m \cdot a_n = a_p \cdot a_q$, then A is a necessary and sufficient condition for B;
4. Let $p, q$ be simple propositions, if "p ∨ q" is a false proposition, then "$\neg p \land \neg q$" is a true proposition. Among these, the numbers of the true propositions are.

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