
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 $A$ be the set of all non-empty subsets of the set $\{1,2, \cdots, n\}$. For $a \in A$, let $\delta(a)$ represent the sum of the elements in $a$. Find $\sum_{a \in A} \delta(a)$.

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