
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 $U=\mathbb{R}$, and the sets $A=\left\{ x\mid y=\ln ({{x}^{2}}-9) \right\}$, $B=\left\{ x\mid \frac{x-7}{x+1} > 0 \right\}$, $C=\left\{ x\mid |x-2| < 4 \right\}$.

Find:
1. $A\cap B$
2. $A\cap {{\complement }_{U}}(B\cap C)$

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