
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 identical vessels have the shape of a right circular cone with a vertical axis; their arrangement and dimensions are shown in diagram 125. Both vessels are filled with water and then emptied through small identical circular openings at the bottom.

Determine the emptying time for each vessel and at what moment the water levels in both vessels will be the same if the emptying started simultaneously.

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