
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 about propositions, the correct ones are __________  
① Given proposition p: $-4 < x-a < 4$, proposition q: $(x-1)(x-3) < 0$, and q is a sufficient but not necessary condition for p, then the range of values for a is $[-1, 5]$;  
② Given proposition p: If $\overrightarrow{a} = (1, 2)$ and $\overrightarrow{b} = (-2, \lambda)$ are collinear, then $\lambda = -4$, proposition q: $\forall k \in \mathbb{R}$, the line $y = kx$ intersects with the circle $x^2 + y^2 - 2y = 0$, then $\neg p \lor q$ is a true proposition;  
③ The negation of the proposition “$\exists x \in \mathbb{R}$, such that $x^2 + x + 1 < 0$” is “$\forall x \in \mathbb{R}$, $x^2 + x + 1 < 0$”;  
④ The contrapositive of the proposition “If $x = v$, then $\cos x = \cos v$” is a true proposition;  
⑤ The converse of the proposition “If $am^2 < bm^2$, then $a < b$” is a true proposition;  
⑥ If $x, y \in \mathbb{R}$, then “$x = y$” is a necessary and sufficient condition for $xy \geq \left( \frac{x+y}{2} \right)^2$;  
⑦ For proposition p: “$\exists x \in \mathbb{R}$, such that $x^2 + x + 1 < 0$”, then $\neg p$: “$\forall x \in \mathbb{R}$, $x^2 + x + 1 \geq 0$”;  
⑧ The negation of the proposition “If $a > b$, then $2^a > 2^b - 1$” is “If $a \leq b$, then $2^a \leq 2^b - 1$”.

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