
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
Let $A = \{x | x \geq 1 \text{ or } x \leq -3\}$, $B = \{x | -4 < x < 0\}$. Find:  
(1) $A \cap B$, $A \cup B$  
(2) $A \cup (\complement_{\mathbb{R}} B)$

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