
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 the function $y=f(x)$, let $A(x\_1,y\_1)$ and $B(x\_2,y\_2)$ be two distinct points on its graph with corresponding tangent line slopes $k\_A$ and $k\_B$. Define $K(A,B)=\frac{|{K}\_{A}-{K}\_{B}|}{|AB|}$ (where $|AB|$ is the length of the line segment $AB$) as the "approximate curvature" of the curve $y=f(x)$ between points $A$ and $B$. For the curve $y=\frac{1}{x}$, let $A\left(a,\frac{1}{a}\right)$ and $B\left(\frac{1}{a},a\right)$ with $a>0$ and $a\neq 1$. If $m\cdot K(A,B)>1$ holds true, find the range of values for the real number $m$.

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