
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 $A = \{x \mid 2a \leq x \leq a + 3\}$ and $B = \{x \mid x < -1 \text{ or } x > 1\}$:
1. If $A \cap B = \emptyset$, find the range of values for $a$.
2. If $A \cup B = \mathbb{R}$, find the range of values for $a$.

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