
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 $A=\{x | 2 \leq x < 7\}$, $B=\{x | 3 < x < 10\}$. Find:<br/>
$(1) A \cap B$; $A \cup B$;<br/>
$(2) (\complement_{\mathbb{R}} A) \cup (\complement_{\mathbb{R}} B)$.

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