
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 $U=\mathbb{R}$, set $A=\{x\mid -2 < x < 5\}$, and set $B=\{x\mid -1 \leqslant x-1 \leqslant 2\}$.

1. Find $A\cup B$ and $A\cap B$.
2. Find $A\cup (B^c)$ and $A\cap (B^c)$, where $B^c$ is the complement of set $B$ with respect to the universal set $U$.

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