
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
(6 points) This question consists of 2 parts, with part 1 worth 4 points and part 2 worth 2 points.  
Given sets $A=\{x\,|\,|x-1|\leq 1\}$, $B=\{x\,|\,x\geq a\}$.  
(1) When $a=1$, find the intersection of sets $A$ and $B$;  
(2) If $A \subseteq B$, find the range of the real number $a$.

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