
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
Given the set $A=\{-5, -4, 0, 6, 7, 9, 11, 12\}$, let $X \subseteq A$, and define $S(x)$ as the sum of the elements in the set $X$. Find the sum of all possible $S(x)$, denoted as $S$.

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