
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
Evaluate $D(72)$, where $D(n)$ denotes the number of ways of representing the positive integer $n$ as a product \[n = f_1 \cdot f_2 \cdots f_k,\] with $k \geq 1$, each $f_i$ an integer greater than $1$, and permutations of the same factors counted separately. For instance, $8$ can be expressed as $8$, $2 \cdot 4$, and $4 \cdot 2$, so $D(8) = 3$.
A) 36
B) 38
C) 40
D) 42

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