
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 $M=\{1,2,3,\ldots,n\}$ ($n\in\mathbb{N}^+$). For any non-empty subset $A$ of $M$, define $f(A)$ as the largest element in $A$. When $A$ ranges over all non-empty subsets of $M$, the sum of the corresponding $f(A)$ is $S_n$. Then: ① $S_3=$ ．② $S_n=$ ．

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