
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]


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For a finite set \( A \) of positive integers, we call a partition of \( A \) into two disjoint nonempty subsets \( A_1 \) and \( A_2 \) 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}
user