
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 two sets $A$ and $B$ that satisfy the conditions $A\cap B \neq \emptyset$ and $A\cup B = \{1, 2, 3, 4, 5\}$. When $A \neq B$, the pair $(A, B)$ and $(B, A)$ are considered as two different pairs of sets. The total number of such set pairs $(A, B)$ that meet the conditions is __________.

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