
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
If you open the cold water tap, the bathtub will fill up in 10 minutes. If you open the hot water tap, it will fill up in 15 minutes. If you remove the plug, the bathtub will completely drain in 12 minutes. How much time will it take to fill the bathtub if both taps are open and the plug is removed?

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