
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 certain supermarket, there are $n$ people waiting in line at the checkout counter. The number of people waiting to check out increases at a fixed rate, and the checkout speed of the cashiers is also fixed. If $2$ checkout counters are open at the same time, the number of people in line can be reduced to $0$ after $20$ minutes. If $3$ checkout counters are open at the same time, the number of people in line can be reduced to $0$ after $12$ minutes. From this, it can be determined that the cashier's checkout speed is ______ times the rate at which the number of people waiting to check out increases.

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