
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 swimming pool has three pipes of different cross-sections for draining water with the help of a uniformly pumping pump. Through the first and second pipes together, with the third pipe closed, the filled pool empties in $a$ minutes; through the first and third pipes together, with the second pipe closed, it empties in $b$ minutes; and through the second and third pipes together, with the first pipe closed, it empties in $c$ minutes. How long does it take to empty the filled pool through each pipe individually?

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