
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
In a store where all items are priced in whole numbers of rubles, there are two special offers:
1) A customer who buys at least three items at once can select one item for free, provided that its price does not exceed the minimum of the paid items' prices.
2) A customer who buys exactly one item priced at no less than \(N\) rubles receives a 20% discount on their next purchase (which can include any number of items).

A customer, visiting this store for the first time, wants to buy exactly four items with a total price of 1000 rubles, where the cheapest item is priced at no less than 99 rubles. Determine the maximum \(N\) such that the second offer is more beneficial for the customer than the first one.

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