
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 \( d(n) \) represent the number of positive divisors of the positive integer \( n \). Define \( f(n)=\frac{d(n)}{\sqrt[3]{n}} \). There exists a unique positive integer \( N \) such that for any positive integer \( n \neq N \), \( f(N) > f(n) \) holds. Find the sum of the digits of \( N \).

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