
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
Consider the following propositions:
1. If both "p ∧ q" and "p ∨ q" are false statements, then "¬p ∧ ¬q" is a true statement.
2. x^2 ≠ y^2 ⇔ x ≠ y or x ≠ -y.
3. The contrapositive of the proposition "If neither a nor b is even, then a + b is not even" is "If a + b is even, then both a and b are even".
4. If the solution set for the real inequality ax^2 + bx + c ≤ 0 is the entire set of real numbers R, then it must be that a < 0 and ∆ ≤ 0.

Identify the correct propositions by listing their numbers.

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