
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 $$A=\{x|x^{2} \geq 4\}, B=\{x| \frac {6-x}{1+x} \geq 0\}, C=\{x||x-3| < 3\}$$, if $U=\mathbb{R}$,  
(1) find $(\complement_{U}B) \cup (\complement_{U}C)$,  
(2) find $A \cap \complement_{U}(B \cap C)$.

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