
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
Ang, Ben, and Jasmin each have four blocks of different colors: red, blue, yellow, and one random color (chosen separately by each from green or white). There are four empty boxes. Each of the people independently places one of their blocks into each box. The probability that at least one box receives 3 blocks all of the same color is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m + n$?
A) 3
B) 33
C) 67
D) 96
E) 128

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