
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
Melinda now has 15 textbooks, 4 of which are mathematics textbooks. She has three empty boxes where one box can hold any four of her textbooks, another can hold any five, and the last can hold any six. If Melinda packs her textbooks into these boxes in random order, find the probability that all four mathematics textbooks end up in the same box. Express this probability as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, and find the sum $m+n$.

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