
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
Let the function $y=f(x)$ have two distinct points on its graph, $A(x_1,y_1)$ and $B(x_2,y_2)$, with the slopes of the tangents at these points being $k_A$ and $k_B$ respectively. Define $\varphi(A,B) = \frac{|k_A - k_B|}{|AB|}$ (where $|AB|$ is the length of segment $AB$) as the "curvature" of the curve $y=f(x)$ between points $A$ and $B$. Identify the true statements from the following and fill in their numbers:

(1) For the function $y=x^3$, if the $x$-coordinates of points $A$ and $B$ are $1$ and $-1$ respectively, then $\varphi(A,B) = 0$;

(2) There exists such a function whose graph has a constant "curvature" between any two points;

(3) If points $A$ and $B$ are two different points on the parabola $y=x^2+1$, then $\varphi(A,B) \leqslant 2$;

(4) For the curve $y=e^x$ (where $e$ is the base of the natural logarithm) and two distinct points $A(x_1,y_1)$ and $B(x_2,y_2)$ on it, then $\varphi(A,B) < 1$.

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