
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: The equation $\frac{x^{2}}{m-2}+\frac{y^{2}}{4-m}=1$ represents an ellipse with foci on the y-axis.
q: The equation $\frac{x^{2}}{3-m}+\frac{y^{2}}{m}=1$ represents a hyperbola.
If $p \vee q$ is true and $p \wedge q$ is false, determine the range of the real number $m$.

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