
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, four of which are mathematics textbooks. The boxes can hold four, five, and six textbooks respectively. If Melinda packs her textbooks into these boxes in random order, the probability that all four mathematics textbooks end up in the same box can be computed as a fraction $\frac{m}{n}$, where $m$ and $n$ are coprime positive integers. Find $m+n$.

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