
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 intelligent raccoons find a stash of nuts. The first raccoon takes some nuts, keeps half of them, and divides the rest equally among the others. The second raccoon takes some nuts, keeps one-third of them, and divides the rest equally among the others. The third raccoon takes some nuts, keeps one-sixth of them, and divides the rest equally among the others. The fourth raccoon takes the remaining nuts, keeps one-twelfth of them, and divides the rest equally among the others. Given that each raccoon receives a whole number of nuts whenever the nuts are divided, and the numbers of nuts the first, second, third, and fourth raccoons have at the end of the process are in the ratio 4:3:2:1, what is the least possible total number of nuts?

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