
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 of dimensions $2\mathrm{ft}\times 4\mathrm{ft}\times 5\mathrm{ft}$ are to be stacked directly on top of each other, with each crate's orientation selected at random. Determine the number of configurations such that the stack of crates reaches exactly $40\mathrm{ft}$ in height.

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