
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) For any non-zero real numbers $a$ and $b$, the inequality $|3a+b|+|a-b|\geqslant |a|(|x+1|+|x-1|)$ always holds. Find the range of values for the real number $x$;

(2) The solution set of the inequality $|2x-1| < 1$ is given as $M$. If $a, b \in M$, compare the size of $\dfrac{{1}}{ab}+{1}$ and $\dfrac{{1}}{a}+\dfrac{{1}}{b}$ and explain the reason.

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