
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
Let the universal set $U=\mathbb{R}$. Given sets $A=\{x \mid |x-a| \leq 1\}$, $B=\{x \mid (4-x)(x-1) \leq 0\}$.

(1) If $a=4$, find $A \cup B$;  
(2) If $A \cap B = A$, find the range of the real number $a$.

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