
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 ways of writing the positive integer $n$ as a product\[n = f_1\cdot f_2\cdots f_k,\]where $k\ge1$, the $f_i$ are integers strictly greater than $1$, and the order in which the factors are listed matters. For example, the number $8$ can be written as $8$, $2 \cdot 4$, $4 \cdot 2$, $2 \cdot 2 \cdot 2$, so $D(8) = 4$. What is $D(72)$?
- **A)** 83
- **B)** 88
- **C)** 93
- **D)** 98
- **E)** 103

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