
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 $d(m)$ denote the number of positive integers that divide $m$, including $1$ and $m$. Define the function $g(m)=\frac{d(m)}{\sqrt[4]{m}}$. Find the unique positive integer $M$ such that $g(M) < g(m)$ for all positive integers $m \ne M$, and calculate the product of the digits of $M$.

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