
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
It is given set  $A=\{1,2,3,...,2n-1\}$ . From set  $A$ , at least  $n-1$  numbers are expelled such that: $a)$  if number  $a \in A$  is expelled, and if  $2a \in A$  then  $2a$  must be expelled $b)$  if  $a,b \in A$  are expelled, and  $a+b \in A$  then  $a+b$  must be also expelled
Which numbers must be expelled such that sum of numbers remaining in set stays minimal

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