
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 \( d(n) \) denote the number of positive integers that divide \( n \), including \( 1 \) and \( n \). Let \( f(n) = \frac{d(n)}{\sqrt[4]{n}} \). There is a unique positive integer \( N \) such that \( f(N) > f(n) \) for all positive integers \( n \neq N \). What is the sum of the digits of \( N \)?
A) 16
B) 17
C) 18
D) 19
E) 20

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