
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
Given the following propositions:
1. If $a$, $b$, $c \in \mathbb{R}$, then "$ac^2 > bc^2$" is a sufficient but not necessary condition for "$a > b$".
2. If the two foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{25} = 1$ are $F_1$ and $F_2$, and the chord $AB$ passes through point $F_1$, then the perimeter of $\triangle ABF_2$ is 16.
3. If the proposition "$\neg p$" and the proposition "$p$ or $q$" are both true, then proposition $q$ must be true.
4. If the proposition $p$ is: There exists an $x \in \mathbb{R}$ such that $x^2 + x + 1 < 0$, then $\neg p$ is: For all $x \in \mathbb{R}$, $x^2 + x + 1 > 0$.

Among these, the true propositions are __________ (fill in the serial numbers).

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