
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 the curve $C$. Consider the following propositions:
$①$ The curve $C$ can never be a circle;
$②$ If $1 < t < 4$, then the curve $C$ is an ellipse;
$③$ If the curve $C$ is a hyperbola, then $t < 1$ or $t > 4$;
$④$ If the curve $C$ is an ellipse with foci on the y-axis, then $1 < t < \frac {5}{2}$.
Determine which of the above statements are true. Write down the numbers of all the correct propositions.

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