
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
Given the function \( d(n) \) as the number of positive integers that divide \( n \), including \( 1 \) and \( n \), and \( f(n) = \frac{d(n)}{\sqrt[4]{n}} \), find the sum of the digits of the unique positive integer \( N \) for which \( f(N) > f(n) \) for all positive integers \( n \neq N \).

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