
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
Given eleven identical crates each with dimensions $3\mathrm{ft}\times 4\mathrm{ft}\times 6\mathrm{ft}$, calculate the probability that a randomly stacked crate tower reaches exactly $50\mathrm{ft}$ in height, assuming each crate's orientation is randomly chosen. Let $\frac {m}{n}$ be this probability with $m$ and $n$ as relatively prime positive integers. Find $m$.

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