
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 vertical cylindrical container, open at the top, is filled with water to the brim. The container is tilted by $30^{\circ}$. How much water spills out of the container if the cylinder has a radius of $10 \mathrm{~cm}$ and a height of $25 \mathrm{~cm}$? Also, find the angle by which the container must be tilted for half of the originally contained water to spill out.

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