
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:
- Proposition p: The equation $\frac{x^{2}}{2m} + \frac{y^{2}}{1-m} = 1$ represents an ellipse with foci on the y-axis.
- Proposition q: The eccentricity $e$ of the hyperbola $\frac{x^{2}}{5} - \frac{y^{2}}{m} = 1$ is in the interval $(1, 2)$. If proposition $p$ implies proposition $q$, find the range of real values for $m$.

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