
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
In the first year of high school, Hua Hua found that for a finite set $A$, it is generally possible to find two non-empty sets $A_{1}$ and $A_{2}$, satisfying $A_{1}$ ⋂ $A_{2}$ = $\varnothing$, and $A_{1} \cup A_{2}$ = $A$. The set $\{A_{1}$, $A_{2}\}$ is called a "partition set" of $A$. If there are $n$ ($n \geq 2$, $n \in N^{*}$) elements in set $A$, then the total number of different "partition sets" is ______. (Fill in the blank with an expression containing $n$)

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