
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]


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Given the equation $\frac{x^2}{4-t} + \frac{y^2}{t-1} = 1$, which represents a curve $C$. Among the following four propositions, select the sequence number(s) of all true propositions.

$①$ If $C$ is an ellipse, then $1$

$②$ If $C$ is a hyperbola, then $t > 4$ or $t < 1$;

$③$ Curve $C$ cannot be a circle;

$④$ If $C$ represents an ellipse with its major axis on the $x$-axis, then $1 < t < \frac{5}{2}$.

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