
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  $n>4$  be a positive integer, which is divisible by  $4$ . We denote by  $A_n$  the sum of the odd positive divisors of  $n$ . We also denote  $B_n$  the sum of the even positive divisors of  $n$ , excluding the number  $n$  itself. Find the least possible value of the expression   $$ f(n)=B_n-2A_n, $$  for all possible values of  $n$ , as well as for which positive integers  $n$  this minimum value is attained.

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