
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
For a finite set  $A$  of positive integers, a partition of  $A$  into two disjoint nonempty subsets  $A_1$  and  $A_2$  is  $\textit{good}$  if the least common multiple of the elements in  $A_1$  is equal to the greatest common divisor of the elements in  $A_2$ . Determine the minimum value of  $n$  such that there exists a set of  $n$  positive integers with exactly  $2015$  good partitions.

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