
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 propositions p and q: 
- Proposition p: There exists an $x_0 \in \mathbb{R}$ such that $x_0 - 2 > 1g x_0$. 
- Proposition q: For all $x \in \mathbb{R}$, $x^2 + x + 1 > 0$.

Evaluate the following conclusions:

1. Proposition "p ∧ q" is true.
2. Proposition "p ∧ (¬q)" is false.
3. Proposition "(¬p) ∨ q" is true.
4. Proposition "p ∨ (¬q)" is false.

Which is/are correct?

A) ②③  
B) ①④  
C) ①③④  
D) ①②③

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