
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
Three clever monkeys divide a pile of bananas. The first monkey takes some bananas from the pile, keeps half of them, and gives one-fourth of the rest to each of the other two monkeys. The second monkey then takes some bananas from the original pile, keeps two-thirds of them, and gives one-sixth of the rest to each of the other two monkeys. The third monkey takes the remaining bananas from the pile, keeps three-quarters of them, and gives one-eighth of the rest to each of the other two monkeys. Given that each monkey receives a whole number of bananas whenever the bananas are divided, and the numbers of bananas the first, second, and third monkeys have at the end of the process are in the ratio $4: 3: 2$, what is the least possible total for the number of bananas?

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