
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 $m \in \mathbb{R}$, let proposition $p: \{m |$ the equation $\frac{y^2}{8-m} + \frac{x^2}{2m-1} = 1$ represents an ellipse with foci on the $y$-axis $\}$, and proposition $q: \{m |$ the equation $\frac{y^2}{m+1} + \frac{x^2}{m-2} = 1$ represents a hyperbola $\}$. If the proposition “$p \lor q$” is true and “$p \land q$” is false, find the range of real numbers $m$.

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