
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]


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In the distant times of the Soviet Union, coins worth 15 and 20 kopecks were in circulation. A student named Valera had a certain amount of money consisting only of these coins. Moreover, the number of 20-kopek coins was greater than the number of 15-kopek coins.
Valera spent one-fifth of all his money by giving away two coins for a movie ticket. He then spent half of the remaining money for lunch, paying with three coins. How many coins of each denomination did Valera originally have? Justify your answer.

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