
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 horizontal cylindrical bucket contains water that occupies one quarter of the circumference of the base. When the bucket is placed upright, what is the ratio of the height of the water to the height of the bucket?

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