
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 $\frac{x^{2}}{4-k} + \frac{y^{2}}{k-1}=1$ is denoted as $C$. Among the following statements:
(1) Curve $C$ cannot be a circle
(2) If $1 < k < 4$, then curve $C$ is an ellipse
(3) If curve $C$ is a hyperbola, then $k < 1$ or $k > 4$
(4) If curve $C$ represents an ellipse with foci on the $x$-axis, then $1 < k < \frac{5}{2}$
The correct statement(s) is/are \_\_\_\_\_\_ (fill in the number(s))

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