
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\[n = f_1 \cdot f_2,\]where the $f_1$ and $f_2$ are integers strictly greater than $1$, and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the number $6$ can be written as $2 \cdot 3$ and $3 \cdot 2$, so $D(6) = 2$. Calculate $D(144)$.
$\textbf{A)}\ 2 \qquad\textbf{B)}\ 4 \qquad\textbf{C)}\ 6 \qquad\textbf{D)}\ 8 \qquad\textbf{E)}\ 10$

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