
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
If \( n \) is a positive integer, \( a(n) \) is the smallest positive integer such that \( (a(n))! \) is divisible by \( n \). Find all positive integers \( n \) such that \( \frac{a(n)}{n} = \frac{2}{3} \). (2003 German Mathematical Olympiad)

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