
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 liquid filtered through a filter evenly flows into a 40-bucket barrel and can flow out through a tap at the bottom of the barrel. If this tap is open, the inflow and outflow of liquid are such that for every 4 minutes, one bucket is reduced in the barrel. How long will it take for the filtered liquid to fill the empty barrel with the bottom tap closed, given that it will take 3 minutes less than the time required for an open tap to pass 66 buckets?

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