
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 $d(n)$ denotes the number of positive integers that divide $n$, including $1$ and $n$ itself, and the function $f(n)=\frac{d(n)}{\sqrt[4]{n}}$, find the smallest positive integer $N$ such that $f(N) \geq f(n)$ for all $n\ne N$ which are not multiples of $N$.

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