
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
Four monkeys divide a pile of bananas. The first monkey takes some bananas from the pile, keeps two-thirds of them, and divides the rest equally between the other three. The second monkey takes some bananas from the remaining pile, keeps one-third of them, and divides the rest equally between the other three. The third monkey then takes some bananas from what's left, keeps one-fourth of them, and divides the rest equally between the other three. The fourth monkey takes the remaining bananas, keeps one-sixth of them, and divides the rest equally among the other three. Given that each monkey receives a whole number of bananas whenever the bananas are divided, and the numbers of bananas the four monkeys have at the end are in the ratio 4:3:2:1, what is the least total number of bananas?

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