
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
Mia, Liam, and Noah each have 6 blocks, colored red, blue, yellow, white, green, and purple; and there are still 5 empty boxes. Each person independently places one of their blocks into each box. The probability that at least one box receives blocks of the same color from at least two different people is $\frac{m}{n}$, where $m$ and $n$ are coprime positive integers. Find $m+n$.
A) 13
B) 17
C) 30
D) 42

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