
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
Definition 1: For a function $f(x)$ ($x \in D$), if there exist two lines $y=kx+m_{1}$ and $y=kx+m_{2}$ with a distance of $d$ between them, such that for $x \in D$, $kx+m_{1} \leqslant f(x) \leqslant kx+m_{2}$ always holds, then the function $f(x)$ is said to have a channel of width $d$ within $D$.

Definition 2: If for a function $f(x)$, for any given positive number $\epsilon$, there exists a real number $x_{0}$, such that the function $f(x)$ has a channel of width $\epsilon$ within $[x_{0}, +\infty)$, then $f(x)$ is said to have an eternal channel at positive infinity. Among the following functions:

1. $f(x)=\ln x$
2. $f(x)= \frac {\sin x}{x}$
3. $f(x)= \sqrt {x^{2}-1}$
4. $f(x)=x^{2}$
5. $f(x)=e^{-x}$

The sequence numbers of the functions that have an eternal channel at positive infinity are $\boxed{2, 3, 5}$.

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