
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 $k \ge 1$, the $f_i$ are integers strictly greater than 1, and the order in which factors are listed matters. For example, the number $10$ can be written as $10$, $2 \cdot 5$, and $5 \cdot 2$, so $D(10) = 3$. What is $D(144)$?
A) 120
B) 126
C) 129
D) 135
E) 140

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