
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
The third Chinese Peking Opera Festival was held in Nanjing. The ticket prices for a certain Peking Opera performance ranged from 2 yuan to over 100 yuan. A group needs to purchase a total of 140 tickets, among which the tickets priced at 6 yuan and 10 yuan. The number of tickets priced at 10 yuan must be at least twice the number of tickets priced at 6 yuan. What is the minimum amount of money required to purchase these two types of tickets, and how many of each should be bought?

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