
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 = \{1,2,3…n\}(n∈N^{})\$, where $N^{}$ is the set of positive integers. For any non-empty subset $A$ of $X\_n$, define $f(A)$ as the maximum element in $A$. When $A$ takes all non-empty subsets of $X\_n$, the corresponding sum of $f(A)$ is denoted as $S\_n$. Determine $S\_n$.

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