
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
There are  $15$  (not necessarily distinct) integers chosen uniformly at random from the range from  $0$  to  $999$ , inclusive. Yang then computes the sum of their units digits, while Michael computes the last three digits of their sum. The probability of them getting the same result is  $\frac mn$  for relatively prime positive integers  $m,n$ . Find  $100m+n$ *Proposed by Yannick Yao*

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