
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 Winter Olympics will be held in Beijing from February 4th to 20th, 2022. A certain store plans to purchase two types of toys, "Bing Dwen Dwen" and "Shuey Rongrong," at the same time. It is known that the cost of 4 "Bing Dwen Dwen" and 5 "Shuey Rongrong" toys is a total of 1000 yuan, and the cost of 5 "Bing Dwen Dwen" and 10 "Shuey Rongrong" toys is a total of 1550 yuan. <br/>① Find the cost of each "Bing Dwen Dwen" and "Shuey Rongrong" toy per unit. <br/>② The store plans to set the selling price of "Bing Dwen Dwen" at 180 yuan per unit and "Shuey Rongrong" at 100 yuan per unit. If the store plans to purchase a total of 180 "Bing Dwen Dwen" and "Shuey Rongrong" toys for sale, and all are sold out, with a minimum profit of 4600 yuan, find how many "Bing Dwen Dwen" toys should be purchased at least?

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