
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 two sets, $A=\{x\mid a\leq x\leq a+3\}$ and $B=\{x\mid (x-6)(x+2)>0\}$:
1. If $A\cap B = \emptyset$, determine the range of values for $a$.
2. If $A\cup B = B$, determine the range of values for $a$.

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