
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 smart monkeys divide a stash of cashews. The first monkey takes some cashews, keeps two-thirds of them, and divides the rest equally between the other two. The second monkey takes some cashews, keeps one-third of them, and divides the rest equally between the other two. The third monkey takes the remaining cashews, keeps one-ninth of them, and divides the rest equally between the other two. All divisions result in whole numbers of cashews, and the final amounts of cashews the first, second, and third monkeys have are in the ratio $3:2:1$. Determine the smallest possible total number of cashews.

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