
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 a Chinese character dictation competition, it is stipulated that the total number of first and second prize winners must not exceed 10 people, the difference between the number of first prize and second prize winners must be less than or equal to 2 people, there must be at least 3 people winning the first prize, and the cost of prizes for first prize is 3 yuan per person, while for second prize it's 2 yuan per person. The minimum cost for purchasing the prizes for this event is ______.

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