
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
Seven dwarfs sat at a round table, each with a mug containing a total of half a liter of milk. (Some of the mugs might have been empty.) One of the dwarfs stood up and distributed the milk in his mug equally to the others. Then, the dwarfs to his right took turns doing the same. After the seventh dwarf redistributed his milk, each mug had exactly the same amount of milk as before the distributions started. How much milk was originally in each mug?

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