
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 the proposition $p$: There exists some $x_{0} \in \mathbb{R}$ such that $mx_{0}^{2} + 1 < 1$, and proposition $q$: For all $x \in \mathbb{R}$, $x^2 + mx + 1 \geq 0$. Determine the range of real numbers $m$ if the disjunction $p \vee (\neg q)$ is false.

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