
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 $b < a < 0$, then among the following results: $① a+b < ab$; $② |a| > |b|$; $③ \dfrac{1}{b} > \dfrac{1}{a} > 0$; $④$ the minimum value of the expression $\dfrac{b}{a} > \dfrac{a}{b}$ is $2$, the correct result numbers are \_\_\_\_\_\_.

(2) If $a > 0$, $b > 0$, and $3a+2b=1$, then the maximum value of $ab$ is \_\_\_\_\_\_.

(3) For two positive numbers $x,y$ satisfying $x+y=4$, the range of real numbers $m$ for which the inequality $\dfrac{1}{x}+\dfrac{4}{y}\geqslant m$ always holds is \_\_\_\_\_\_\_\_\_\_.

(4) Given $x\ne 0$, the function $y={(x+\dfrac{1}{x})}^{2}-1$ has its minimum value at $x=$ \_\_\_\_\_\_\_\_ and the minimum value is \_\_\_\_\_\_\_\_\_\_.

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