
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 sets $A=\{x \mid |x-4| \leq 2\}$, and $B=\left\{x \mid \frac{5-x}{x+1} > 0\right\}$, with the universal set $U=\mathbb{R}$.  
(1) Find $A \cap (\complement_U B)$.  
(2) If the set $C=\{x \mid x < a\}$, and $A \cap C \neq \emptyset$, find the range of the real number $a$.

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