
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 dwarves are sitting at a round table. In front of each of them is a mug of milk. One of the dwarves pours $1/4$ of his milk to the neighbor on the right. Then the neighbor on the right does the same. Then the next neighbor on the right does the same, and finally, the fourth dwarf pours $1/4$ of his milk to the first dwarf. There is a total of 2 liters of milk in all the mugs together. How much milk was originally in the mugs if

a) in the end, all dwarves have the same amount of milk?

b) in the end, each dwarf has as much milk as they had in the beginning?

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