
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, $\frac{1}{4}$ of the water previously in the first barrel will remain. If the third barrel is then filled with water from the second barrel, $\frac{2}{9}$ of the water previously in the second barrel will remain.

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 up completely. Determine the capacity of each barrel.

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