
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 pool has three inlets and one outlet. If we open the outlet and two of the inlets simultaneously, it takes 6 hours, 5 hours, and 4 hours respectively to fill the pool completely. If we open the outlet and all three inlets simultaneously, it takes 3 hours to fill the pool. How many hours will it take to fill the pool if we open all three inlets simultaneously without opening the outlet?

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