
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 $x_n = \{1, 2, \ldots, n\}$ ($n \in \mathbb{N}_+$), for any non-empty subset $A$ of $x_n$, define $f(A)$ as the smallest element in $A$. When $A$ ranges over all non-empty subsets of $x_n$, 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}
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