
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 a function $f(x)=|2x+a|+|x-b|$,
$(1)$ When $a=-2$, $b=1$, find the solution set of the inequality $f(x) < 6$;
$(2)$ If $a > 0$, $b > 0$, and the minimum value of $f(x)$ is $1$, find the minimum value of $\dfrac{2}{a}+ \dfrac{1}{b}$.

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