
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 has three empty boxes and 15 textbooks, three of which are mathematics textbooks. The boxes can hold 3, 5, and 7 textbooks respectively. If Melinda packs her textbooks into these boxes in random order, what is the probability that all three mathematics textbooks end up in the same box? Express your answer as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, and then find $m+n$.

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