
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
In a laboratory setup, a certain liquid flows into a vessel through three inlet taps. If all taps are opened simultaneously, the vessel will be filled in 6 minutes. If only the second tap is used to fill the vessel, it will take 0.75 of the time it takes for the vessel to be filled by only the first tap. Using only the third tap, the vessel fills 10 minutes longer than it would with just the second tap. For how long would each tap need to be open individually to fill the vessel?

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