
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
1. For all $x \in \mathbb{R}$, $x^2 + 2x + 7 > 0$; 
2. There exists an $x \in \mathbb{R}$ such that $x + 1 > 0$; 
3. If "if not $p$ then not $q$" is true, then "if $q$ then $p$" is also true; 
4. Let proposition $p$: $\phi$ is a subset of any set, proposition $q$: $0 \in \phi$, then $p \lor q$ is true, and $p \land q$ is false. Among these four propositions, the correct ones are.

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