
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, where p: There exists an x ∈ ℝ such that mx^2 + 1 ≤ 0, and q: For all x ∈ ℝ, x^2 + mx + 1 > 0. If the proposition p ∨ q (either p or q is false), find the range of real numbers m.

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