
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 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 two. The second monkey takes the remaining bananas from the pile, keeps one-fifth of them, and divides the rest equally between the other two. The third monkey takes what's left, keeps one-tenth of them, and divides the rest equally between the other two. Each division leads to whole number of bananas for each monkey. Given that the quantities of bananas held by the first, second, and third monkeys at the end are in the ratio $4:2:1$, determine the smallest initial number of bananas.

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