
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
Suppose you have two bank cards for making purchases: a debit card and a credit card. Today, at the beginning of the month, you decide to buy airline tickets costing 12,000 rubles. If you make the purchase with the credit card (assuming the credit limit allows), you will need to repay the bank in $\mathrm{N}$ days to stay within the grace period during which the credit can be repaid without additional fees. Additionally, in this case, the bank will give a cashback of $1\%$ of the purchase amount after 1 month. If you make the purchase with the debit card (assuming there are sufficient funds), you will receive a cashback of $2\%$ of the purchase amount after 1 month. It is known that the annual interest rate on the average monthly balance of funds on the debit card is $6\%$ per annum (for simplicity, assume each month has 30 days, interest is paid at the end of each month, and accumulated interest on the balance is not compounded). Determine the maximum number of days $\mathrm{N}$ such that, under equal conditions, it is more advantageous to pay for the airline tickets with the debit card.

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