
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
Given that $A$ and $B$ are the endpoints of the graph of the function $y=f(x)$, where $x\in[a,b]$, and $M(x,y)$ is any point on the graph of $f(x)$, where $x=\lambda a+(1-\lambda)b$, $\lambda\in[0,1]$. It is also known that the vector $\overrightarrow{ON}=\lambda \overrightarrow{OA}+(1-\lambda) \overrightarrow{OB}$. If the inequality $|\overrightarrow{MN}|\leqslant k$ always holds, then the function $f(x)$ is said to be "k-order linearly approximated" on $[a,b]$. If the function $f(x)=x- \frac {1}{x}$ is "k-order linearly approximated" on $[1,2]$, then the range of values for the real number $k$ is ______.

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