
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 the olympiad, each solved problem could earn 3, 8, or 10 points. Vasya scored 45 points. What is the minimum number of problems he could have solved? (It is necessary to explain why he could not have solved fewer problems.)

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