
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 \( n \). Define a function \[ g(n) = \frac{d(n)^2}{\sqrt[4]{n}}. \] Find the positive integer \( M \) such that \( g(M) > g(m) \) for all positive integers \( m \neq M \). What is the sum of the digits of \( M \)?
A) 5  
B) 6  
C) 8  
D) 12  
E) 9

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