
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 $a_{i}(i=1,2,3)$ be real numbers. If the sum of all non-empty proper subsets of the set $\{a_{1}, a_{2}, a_{3}\}$ is $12$, then $a_{1}+a_{2}+a_{3}=$____.

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