
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 \(S\) be the set of all positive integer divisors of \(72,000\). How many numbers are the product of two distinct elements of \(S\)?
A) 445
B) 451
C) 460
D) 470

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