
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: Proposition p: The equation $$\frac {x^{2}}{2m}+ \frac {y^{2}}{15-m}=1$$ represents an ellipse with foci on the y-axis. Proposition q: The hyperbola $$\frac {y^{2}}{2}- \frac {x^{2}}{3m}=1$$ has an eccentricity $e$ in the range $(2, 3)$. If $p \lor q$ is true and $p \land q$ is false, find the range of the real number $m$.

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