
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
At a market in Egypt, a tourist is negotiating with a seller for a souvenir worth 10,000 Egyptian pounds. The tourist first reduces the price by \( x \) percent \((0 < x < 100)\), then the seller increases the price by \( x \) percent, and so on. The value of \( x \) does not change during the bargaining process, and the seller increases the price at least once. The negotiation continues until one of the participants gets a non-integer value for the price of the souvenir. Find the largest possible number of price changes during such a negotiation (including the last non-integer price change).

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