
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
A 3-element set \( S \) has the sum of the elements of all its subsets equal to 2012 (consider the sum of elements of the empty set to be zero). What is the sum of the elements of \( S \) equal to?

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