
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 $P$ states that the equation $\frac{x^{2}}{2m} + \frac{y^{2}}{9-m} = 1$ represents an ellipse with its foci on the $y$-axis, and $Q$ states that the eccentricity $e$ of the hyperbola $\frac{y^{2}}{5} - \frac{x^{2}}{m} = 1$ is within the range $(\frac{\sqrt{6}}{2}, \sqrt{2})$. If only one of the propositions $P$ and $Q$ is true, find the range of values for the real number $m$.

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