
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 finite set of positive integers  $A$  is called *meanly* if for each of its nonempy subsets the arithmetic mean of its elements is also a positive integer. In other words,  $A$  is meanly if  $\frac{1}{k}(a_1 + \dots + a_k)$  is an integer whenever  $k \ge 1$  and  $a_1, \dots, a_k \in A$  are distinct.

Given a positive integer  $n$ , determine the least possible sum of the elements of a meanly  $n$ -element set.

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