
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 $f(x)=x+\dfrac{a}{x}-4$, $g(x)=kx+3$.

(Ⅰ) For any $a \in [4,6]$, the maximum value of $|f(x)|$ in the interval $[1,m]$ is $|f(x)|$. Find the range of values for the real number $m$.

(Ⅱ) For any $a \in [1,2]$, if the inequality $|f(x_{1})|-|f(x_{2})| < g(x_{1})-g(x_{2})$ always holds for any $x_{1}, x_{2} \in [2,4]$ ($x_{1} < x_{2}$), find the range of values for the real number $k$.

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