
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
When valves A, B, and C are opened together, it takes 12 minutes to fill the entire pool; when valves B, C, and D are opened together, it takes 15 minutes to fill the entire pool; when valves A and D are opened together, it takes 20 minutes to fill the pool. How long will it take to fill the pool if all four valves are opened together?

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