
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

Calculation-loving Samson likes to have lunch at the Italian restaurant "Pablo's." On his next visit to the restaurant, Samson was offered to purchase a one-year loyalty card for 30,000 rubles, which gives a 30% discount on the bill.

(a) Suppose Samson visits the restaurant three times a week (regardless of whether he has the loyalty card or not) with an average check amount of 900 rubles, without considering any discounts. Is it beneficial for him to purchase the loyalty card?

(b) According to the information portal, the average bill amount per person in this restaurant is 600 rubles. On average, how many visits per year does a client need to make for it to be indifferent whether they buy the restaurant's loyalty card or not?

(c) Recently, many stores and service organizations have been issuing so-called customer cards. Some of these cards accumulate discounts after a certain amount is spent, while others provide an immediate discount for any purchase. Provide at least two strong reasons, with arguments, why it is advantageous for retail and service enterprises to implement such cards and use them while working with customers.

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