
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 that $p$: $\forall x \in \mathbb{R}, 2x > m(x^2 + 1)$ and $q$: $\exists x_0 \in \mathbb{R}$ such that $x_0^2 + 2x_0 - m - 1 = 0$, and both $p$ and $q$ are true, determine the range of real numbers $m$.

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