
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
The equation $$\frac{x^2}{4-t} + \frac{y^2}{t-1} = 1$$ represents a curve C. Consider the following four propositions:  
① The curve C cannot be a circle;  
② If curve C is an ellipse, then $1<t<4$;  
③ If curve C is a hyperbola, then $t<1$ or $t>4$;  
④ If curve C represents an ellipse with foci on the x-axis, then $1<t<\frac{5}{2}$.  
The correct propositions are ________________.

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