
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
For a function $f(x)$ defined on domain $D$, if there exist two lines $y=kx+m_1$ and $y=kx+m_2$ with a distance of $d$ between them, such that for any $x \in D$, the inequality $kx+m_1 \leqslant f(x) \leqslant kx+m_2$ holds, then the function $f(x)$ ($x \in D$) is said to have a channel of width $d$. Consider the following functions:

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

Among these functions, on the interval $[1,+\infty)$ those that can have a channel width of $1$ are __________ (write down all correct indexes).

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