
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 $A=\{x\in Z\mid |x| < 6\}$, $B=\{1,2,3\}$, $C=\{3,4,5\}$, find:
$(1) B\cap C$; $(2) B\cup C$; $(3) A\cup (B\cap C)$; $(4) A\cap \lnot_{A}(B\cup C)$

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