
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 solution set of the inequality $|x-1| \leq a$ ($a > 0$) is $A$, and the domain of the function $f(x) = \log \frac{x-2}{x+2}$ is $B$.
(1) If $a=2$, find $A \cap B$;
(2) If $A \cap B = \emptyset$, find the range of $a$.

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