
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
Fifteen identical crates each with dimensions $2\mathrm{ft}\times 3\mathrm{ft}\times 5\mathrm{ft}$ are stacked. Each crate's orientation is chosen at random. Calculate the probability that the stacked height is exactly $50\mathrm{ft}$ tall. Express the probability as a reduced fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers.

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