
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
Define the function \( g(n) = \frac{d(n)}{\sqrt[4]{n}} \) where \( d(n) \) represents the number of positive divisors of \( n \), including \( 1 \) and \( n \). We look for a unique positive integer \( M \) such that \( g(M) > g(n) \) for all \( n \neq M \). What is the sum of the digits of \( M \)?
A) 5
B) 6
C) 7
D) 8
E) 9

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