
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 curious raccoons find a cache of nuts. The first raccoon takes some nuts from the cache, keeps five-sixths of them, and distributes the rest equally between the other two. The second raccoon takes some nuts from the cache, keeps one-third of them, and distributes the rest equally between the other two. The third raccoon takes the remaining nuts from the cache, keeps one-eighth of them, and distributes the rest equally between the other two. Given that each raccoon receives a whole number of nuts whenever nuts are distributed, and the numbers of nuts the first, second, and third raccoons have at the end of the process are in the ratio $4:3:2$, what is the least possible total for the number of nuts?

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