
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
The bathtub fills with cold water in 6 minutes 40 seconds and with hot water in 8 minutes. Additionally, if the plug is removed from a full bathtub, the water will drain out in 13 minutes 20 seconds. How long will it take to fill the bathtub completely, given that both taps are open but the bathtub is not plugged?

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