
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 following two propositions, proposition p: The equation $$\frac {x^{2}}{25-m} + \frac {y^{2}}{m-7} = 1$$ represents an ellipse with foci on the x-axis. Proposition q: The eccentricity $e$ of the hyperbola $$\frac {y^{2}}{5} - \frac {x^{2}}{m} = 1$$ belongs to the interval (1, 2). It is known that $\neg p \lor \neg q$ is false, find the range of the real number $m$.

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