
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 $A$ and $B$ be two non-empty sets. The difference between $A$ and $B$ is defined as $A - B = \{x \mid x \in A \text{ and } x \notin B\}$.
(1) Give two number sets and find their difference;
(2) Are the differences $A - B$ and $B - A$ always equal? Explain your answer;
(3) Given $A = \{x \mid x > 4\}$ and $B = \{x \mid -6 < x < 6\}$, find $A - (A - B)$ and $B - (B - A)$.

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