
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 universal set $I=\mathbb{R}$, $A=\{x\in\mathbb{R}|-1 < x \leqslant 2\}$, $B=\{x\in\mathbb{R}|x < a\}$.  
$(1)$ Find $\complement_{I}A$;  
$(2)$ If $A\cap B \neq \varnothing$, find the range of the real number $a$;  
$(3)$ If $A\cup B = B$, find the range of the real number $a$.

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