
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  $F$  be the set of all  $n-tuples$   $(A_1,A_2,…,A_n)$  such that each  $A_i$  is a subset of  ${1,2,…,2019}$ . Let  $\mid{A}\mid$  denote the number of elements o the set  $A$  . Find  $\sum_{(A_1,…,A_n)\in{F}}^{}\mid{A_1\cup{A_2}\cup...\cup{A_n}}\mid$ 

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