
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 the set $U=\{1,2,…,n\}$ ($n\in\mathbb{N}^*$, $n\geqslant 2$), for two non-empty subsets $A$, $B$ of set $U$, if $A\cap B=\varnothing$, then the pair $(A,B)$ is called a "mutually exclusive subset pair" of set $U$. Let $f(n)$ denote the number of all "mutually exclusive subset pairs" of set $U$ (considering $(A,B)$ and $(B,A)$ as the same "mutually exclusive subset pair").
- (1) Write down the values of $f(2)$, $f(3)$, $f(4)$;
- (2) Find $f(n)$.

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