
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 physics textbooks. One box will hold any four of her textbooks, another will hold any five, and the largest one will hold any six of her textbooks. If Melinda packs her textbooks into these boxes randomly, what is the probability that all four physics textbooks end up in the same box? Express the probability in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, and find $m+n$.

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