
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 is being filled by three pipes. The first and second pipes together can fill the pool in 70 minutes, the first and third pipes together can fill it in 84 minutes, and the second and third pipes together can fill it in 140 minutes. How many minutes will it take to fill the pool using each pipe individually, and how many minutes will it take if all three pipes are open at the same time?

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