
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
 $A$  and  $B$  wrote two positive integers respectively in a black board. The product of the numbers written by  $A$  was twice as the sum of the numbers written by  $B$  and the product of the numbers written by  $B$  was twice as the sum of the numbers written by  $A$  and the sum of the numbers written by  $A$  is more than or equal to that of  $B$ . Find all possible sum written by  $B$ .
Note: Four numbers written are not always distinct.

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