
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
Eight identical crates each of dimensions $2\mathrm{ft}\times 5\mathrm{ft}\times 7\mathrm{ft}$. The first crate is placed flat on the floor. Each of the remaining seven crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen at random. Find the probability that the stack of crates is exactly $36\mathrm{ft}$ tall.

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