
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
Promotion. The store "Crocus and Cactus" announced a promotion: if a customer buys three items, the cheapest one among them is free. The customer picked ten items, all at different prices: 100 rubles, 200 rubles, 300 rubles, and so on, with the most expensive item costing 1000 rubles.

a) What is the minimum amount the customer will pay if they arrange their purchases optimally?

b) What is the maximum amount the customer will pay if they arrange their purchases suboptimally?

c) Find the expected value of the amount the customer will pay if they arrange the purchases randomly.

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