
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 $A=\{x \mid |x-a| \leq 1\}$ and $B=\{x \mid x^2 - 5x + 4 \leq 0\}$.  
(1) When $a=1$, find $A \cup B$.  
(2) It is known that "$x \in A$" is a sufficient condition for "$x \in B$". Determine the range of values for the real number $a$.

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