
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 four empty boxes and 15 textbooks, four of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any five of her textbooks, one will hold any four of her textbooks, and one will hold any three of her textbooks. If Melinda packs her textbooks into these boxes in a random order, the probability that all four mathematics textbooks end up in the same box can be written as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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