
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 the outlet and any two of the inlets are opened simultaneously, the pool takes 6 hours, 5 hours, and 4 hours to fill separately. If the outlet and all three inlets are opened simultaneously, it takes 3 hours to fill the pool. How long will it take to fill the pool if all three inlets are opened without opening the outlet?

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