
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
A container is already filled with water. There are three lead balls: large, medium, and small. The first time, the small ball is submerged in the water; the second time, the small ball is removed, and the medium ball is submerged in the water; the third time, the medium ball is removed, and the large ball is submerged in the water. It is known that the water spilled the first time is 3 times the water spilled the second time, and the water spilled the third time is 3 times the water spilled the first time. Find the ratio of the volumes of the three balls.

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