
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 $\sigma(n)$ denote the sum of all positive divisors of $n$. Define the function\[g(n) = \frac{\sigma(n)}{n}.\]Find the smallest integer $N$ such that $g(N)$ is greater than $g(n)$ for all $n \neq N$ with $1 \leq n \leq 100$.
A) 2
B) 6
C) 12
D) 28
E) 30

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