
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
One of three barrels is filled with water, while the other two are empty. If the second barrel is filled with water from the first barrel, then $1 / 4$ of the water remains in the first barrel. If the third barrel is then filled with water from the second barrel, then $2 / 9$ of the water remains in the second barrel. Finally, if the water from the third barrel is poured into the empty first barrel, it will require an additional 50 buckets to fill it. Determine the capacity of each barrel.

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