
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 waiter at the restaurant U Šejdíře always adds the current date to the bill: he increases the total amount spent by as many crowns as the day of the month it is.

In September, a group of three friends dined at the restaurant twice. The first time, each person paid separately, and the waiter added the date to each bill, resulting in each person being charged 168 CZK. Four days later, they had lunch again and ordered exactly the same as before. This time, however, one person paid for all three. The waiter added the date to the bill only once and asked for 486 CZK in total. The friends were puzzled that although the prices on the menu had not changed, the lunch was cheaper this time, and they uncovered the waiter’s scam. What was the date?

(Hint: Determine what their total bill would have been if each person paid separately the second time as well.)

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