
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
Twelve identical crates each with dimensions $3\mathrm{ft} \times 4\mathrm{ft} \times 5\mathrm{ft}$. The first crate is placed flat on the floor. Each of the remaining eleven crates is placed in turn flat on top of the previous crate, and the orientation of each crate is chosen at random. Find the number of ways to stack the crates such that the total height is exactly $50\mathrm{ft}$.

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