
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 \( X_n = \{1, 2, \cdots, n\} \). For any subset \( A \) of \( X_n \), let \( f(A) \) be the smallest element in \( A \). Calculate \( \sum_{A \subseteq X_n} f(A) \).

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