
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
Dragon selects three positive real numbers with sum  $100$ , uniformly at random.  He asks Cat to copy them down, but Cat gets lazy and rounds them all to the nearest tenth during transcription.  If the probability the three new numbers still sum to  $100$  is  $\tfrac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers, compute  $100m+n$ .

*Proposed by Aaron Lin*

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