
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 set $A=\{x||x-4| \lt 2x\}$ and set $B=\{x|x(x-a)\geqslant (a+6)(x-a)\}$. Choose one of the following conditions to solve, and the answer should not be empty.<br/>① If $A$⋂$B=A$, find the range of real number $a$;<br/>② If $A$⋂$B=B$, find the range of real number $a$.

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