
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
A student had some coins with denominations of 15 kopecks and 20 kopecks, and there were more 20 kopeck coins than 15 kopeck coins. The student spent a fifth of all the money by giving away two coins for movie tickets. Half of the remaining money was spent on lunch, which was paid with three coins. How many coins of each denomination did the student have initially?

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