
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
For any $n$-element set $S_{n}$, if its subsets $A_{1}$, $A_{2}, \cdots, A_{k}$ satisfy $\bigcup_{i=1}^{k} A_{i}=S_{n}$, then the unordered set $\left(A_{1}, A_{2}, \cdots, A_{k}\right)$ is called a "k-order partition" of the set $S_{n}$. What is the number of 2-order partitions of $S_{n}$?

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