
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 sets $A=\{x|2^{x}\geqslant 16\}$, $B=\{x|\log_{2}x\geqslant a\}$.
$(1)$ When $a=1$, find $A\cap B$;
$(2)$ If $A$ is a subset of $B$, find the range of the real number $a$.

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