
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
(1) If $1 < a < 8$ and $-4 < b < 2$, then the range of values for $a-|b|$ is _______.

(2) If the solution set of the inequality $|x-3|+|x-4| < a$ with respect to $x$ is empty, then the range of values for the real number $a$ is _______.

(3) In the Cartesian coordinate system $xoy$, with $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. Given that the polar equation of line $l$ is $\rho (\sin \theta -3\cos \theta )=0$, and the equation of curve $C$ is $\begin{cases} x=t-\dfrac{1}{t}, \\ y=t+\dfrac{1}{t} \end{cases}$ (where $t$ is a parameter), $l$ and $C$ intersect at points $A$ and $B$, and $|AB|=$ _______.

(4) Let $n$ be a positive integer, and $f(n)=1+ \dfrac{1}{2}+ \dfrac{1}{3}+…+ \dfrac{1}{n}$. It is calculated that $f(2)= \dfrac{3}{2}$, $f(4) > 2$, $f(8) > \dfrac{5}{2}$, $f(16) > 3$. Observing the above results, a general conclusion can be inferred as _______.

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