
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 24th Winter Olympics was held in Beijing and Zhangjiakou, China from February 4, 2022 to February 20, 2022. This was the first time China hosted the Winter Olympics. The Winter Olympics mascots "Bing Dwen Dwen" and "Shuey Rhon Rhon" ceramic products are available in small and large sets. It is known that buying 2 small sets costs $20 less than buying 1 large set; buying 3 small sets and 2 large sets costs a total of $390.  
$(1)$ Find the unit prices of these two sets.  
$(2)$ A school plans to use $1500 to purchase a total of 20 sets of these ceramic products, both small and large, as prizes. How many large sets can the school purchase at most?

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