
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

Experts predict that apartment prices in Moscow will drop by $20\%$ in rubles and $40\%$ in euros in a year. In Sochi, apartment prices will decrease by $10\%$ in rubles in a year. By how much will apartment prices in Sochi decrease in euros? Assume that the exchange rate between euros and rubles (i.e., the price of one euro in rubles) is the same in both Moscow and Sochi, although it may change over time. Justify your answer.

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