
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 $p$: The hyperbola $\frac{y^2}{5} - \frac{x^2}{m} = 1$ has an eccentricity $e\in\left(\frac{\sqrt{6}}{2}, \sqrt{2}\right)$, and the proposition $q$: The equation $\frac{x^2}{2m} + \frac{y^2}{9-m}=1$ represents an ellipse with foci on the x-axis, if "$p$ or $q$" is a true proposition and "$p$ and $q$" is a false proposition, find the range of the real number $m$.

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