
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
Jessica has four empty boxes and 15 textbooks, four of which are English textbooks. The first box will hold any three of her textbooks, the second will hold any four of her textbooks, the third will hold any five of her textbooks, and the fourth will hold any three of her textbooks. If Jessica packs her textbooks into these boxes in random order, the probability that all four English textbooks end up in the third box can be written as $\frac{m}{n}$, 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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