
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 the factors are listed matters. Also, suppose each representation must include at least one term divisible by 5. Calculate $D(120)$.
A) 19
B) 21
C) 24
D) 26

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