
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 water tank with a capacity of $120 \mathrm{hl}$ has three pipes: the first two fill the tank, and the third one drains it. The first pipe fills the tank one hour faster than the second. When the first and third pipes are open, the tank fills in $7 \frac{1}{2}$ hours. When the second and third pipes are open, the tank fills in 20 hours. How many hours does it take to fill the tank if all three pipes are open simultaneously?

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