
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 the integer $n \geq 3$, and let $P = \{1, 2, \ldots, n\}$. $A$ and $B$ are two non-empty subsets of $P$. The number of pairs of sets $(A, B)$ such that the maximum number in $A$ is less than the minimum number in $B$ is: ______.

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