
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 states that the equation $$\frac {x^{2}}{2m}- \frac {y^{2}}{m-2}=1$$ represents a hyperbola with foci on the x-axis. Proposition q states that the curve $y=x^2+(2m-3)x+1$ intersects the x-axis at two distinct points. If the conjunction of p and q (p∧q) is a false proposition, and their disjunction (p∨q) is a true proposition, find the range of the real number $m$.

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