
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 curve represented by the equation $\frac{x^2}{4-t} + \frac{y^2}{t-1} = 1$ is denoted as $C$. The following four statements are given:
$①$ If $C$ is an ellipse, then $1 < t < 4$;
$②$ If $C$ is a hyperbola, then $t > 4$ or $t < 1$;
$③$ The curve $C$ cannot be a circle;        
$④$ If $1 < t < \frac{5}{2}$, the curve $C$ is an ellipse, and its foci have coordinates $(± \sqrt{5-2t}, 0)$;
$⑤$ If $t < 1$, the curve $C$ is a hyperbola, and its imaginary axis length is $\sqrt{1-t}$.
Among these, the true statements are numbered ___. (Fill in all correct statement numbers on the line).

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