
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]


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Let  $A$  and  $B$  be two sets of non-negative integers, define  $A+B$  as the set of the values obtained when we sum any (one) element of the set  $A$  with any (one) element of the set  $B$ . For instance, if  $A=\{2,3\}$  and  $B=\{0,1,2,5\}$  so  $A+B=\{2,3,4,5,7,8\}$ .
Determine the least integer  $k$  such that there is a pair of sets  $A$  and  $B$  of non-negative integers with  $k$  and  $2k$  elements, respectively, and $A+B=\{0,1,2,\dots, 2019,2020\}$ 

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