
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
Schoolboy Alexey told his parents that he is already an adult and can manage his finances independently. His mother suggested using a duplicate bank card from her account. For participation in a charitable Christmas program, Alexey wants to buy 40 "Joy" chocolate bars and donate them to an orphanage. However, the bank, where Alexey's parents are clients, has implemented a new system to protect against unauthorized card payments. The protection system analyzes the root mean square (RMS) value of expenses for the last 3 purchases (S) using the formula \(S=\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}{3}}\), where \(x_{1}, x_{2}\), and \(x_{3}\) are the costs of the previous purchases, and compares the value of \(S\) with the cost of the current purchase. If the cost of the current payment exceeds the value \(S\) by 3 times, the bank blocks the payment and requires additional verification (e.g., a call from mom to the call center). In the last month, payments made on the card were only for cellphone bills in the amount of 300 rubles each. Into how many minimum number of receipts should Alexey split the purchase so that he can buy all 40 "Joy" chocolate bars at a cost of 50 rubles each?

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