
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 proposition p: The equation $\frac {x^{2}}{2k-1}+ \frac {y^{2}}{k-1}=1$ represents an ellipse; and the proposition q: The equation $\frac {x^{2}}{4-k}+ \frac {y^{2}}{k-3}=1$ represents a hyperbola. If "p or q" is true and "p and q" is false, find the range of the real number k.

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