
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 oil barrel has oil inside occupying $\frac{1}{4}$ of the circumference of its base. Find the ratio of the height of the oil to the height of the barrel when the barrel is standing upright.

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