
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 $f(x)=|x+2a|+|x-1|$.
$(1)$ If $a=1$, solve the inequality $f(x)\leqslant 5$;
$(2)$ When $a\neq 0$, let $g(a)=f\left( \dfrac {1}{a}\right)$, find the range of values of $a$ for which $g(a)\leqslant 4$.

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