
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. "m ∈ (-1, 2)" is a necessary and sufficient condition for the equation $\frac{x^2}{m+1} - \frac{y^2}{m-2} = 1$ to represent an ellipse.
2. The contrapositive of the proposition "If the absolute difference in distances from a moving point P to two fixed points F₁(-4, 0) and F₂(4, 0) is 8, then the trajectory of P is a hyperbola" is true.
3. If the compound statement "p ∧ q" is false, then both p and q are false statements.
4. Given the conditions p: {x | x < -3 or x > 1} and q: x > a. If ¬p is a sufficient but not necessary condition for ¬q, then the range of the real number a is a ≥ 1.

The correct proposition(s) is/are _______.

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