
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
Which of the following four propositions is true:
1. For all $x \in \mathbb{R}$, $2x^2 - 3x + 4 > 0$.
2. For all $x \in \{-1, 0, 1\}$, $2x + 1 > 0$.
3. There exists $x \in \mathbb{N}$ such that $x^2 \leq x$.
4. There exists $x \in \mathbb{N}$ such that $x$ is a divisor of $29$.

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