
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
For any non-empty subset  $A$  of  $\{1, 2, \ldots , n\}$  define  $f(A)$  as the largest element of  $A$  minus the smallest element of  $A$ . Find  $\sum f(A)$  where the sum is taken over all non-empty subsets of  $\{1, 2, \ldots , n\}$ .

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