
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
At a supermarket, there are $n$ people waiting in line at the checkout counter. The number of people checking out increases at a fixed rate, and the speed at which the cashiers check out customers is also fixed. If $2$ checkout counters are open at the same time, it takes $20$ minutes to clear the line. If $3$ checkout counters are open at the same time, it takes $12$ minutes to clear the line. To reduce the waiting time for customers to checkout to zero within $6$ minutes, at least how many checkout counters need to be open?

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