
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 set $A=\{x|0 < ax+1\leqslant 3\}$, and the set $B=\left\{ x|-\dfrac{1}{2} < x < 2 \right\}$.

   $(1)$ If $a=1$; find ${{\complement }_{A}}B$;

   $(2)$ If $(A\cap B=A)$, find the range of the real number $a$.

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