
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
Two vases are cylindrical in shape. The larger vase has a diameter of $20 \text{ cm}$. The smaller vase has a diameter of $10 \text{ cm}$ and a height of $16 \text{ cm}$. The larger vase is partially filled with water. Then the empty smaller vase, with the open end at the top, is slowly pushed down into the water, which flows over its rim. When the smaller vase is pushed right down, it is half full of water. What was the original depth of the water in the larger vase?
A) $10 \text{ cm}$
B) $12 \text{ cm}$
C) $14 \text{ cm}$
D) $16 \text{ cm}$
E) $18 \text{ cm}$

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