
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 purchased a total of 180 Winter Olympics commemorative items, including "Bing Dwen Dwen" figurines and pendants. It is known that the cost price of a "Bing Dwen Dwen" figurine is $80 per item, and the cost price of a "Bing Dwen Dwen" pendant is $50 per item.  
$(1)$ If the store spent a total of $11400 on purchasing the "Bing Dwen Dwen" figurines and pendants, please find the quantities of each item purchased.  
$(2)$ The store plans to set the selling price of a "Bing Dwen Dwen" figurine at $100 per item and the selling price of a "Bing Dwen Dwen" pendant at $60 per item. If all 180 "Bing Dwen Dwen" figurines and pendants are sold out, and the store wants to make a profit of at least $2900, find the maximum number of "Bing Dwen Dwen" pendants that can be purchased.

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