
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
Consider the propositions p and q, where p states that the solution set for the inequality $|x| + |x + 1| > m$ is $\mathbb{R}$, and q states that the function $f(x) = x^2 - 2mx + 1$ is increasing on the interval $(2, +\infty)$. If the disjunction p ∨ q is true and the conjunction p ∧ q is false, find the range of real numbers m.

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