
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
Eight dwarves are seated around a circular table, each with three diamonds. The dwarves' seats are numbered sequentially from 1 to 8. Every minute, the dwarves simultaneously do the following: they divide all their diamonds into two piles (one or both of the piles can be empty), then give one pile to their left neighbor and the other pile to their right neighbor. At a certain point, all the diamonds are gathered among three of the dwarves. One of the dwarves ended up with 7 diamonds. How many diamonds do each of the other two have?

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