
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 $A=\{x|x=a_0+a_1\times2+a_2\times2^2+a_3\times2^3\}$, where $a_i\in\{0,1,2\}$ ($i=0,1,2,3$), and $a_0\neq0$, find the sum of all elements in set $A$.

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