
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
Go originated in China, known as "Yi" in ancient times, is the ancestor of chess games. Go has a history of more than four thousand years. Chinese chess is also a cultural treasure of the Chinese nation, with a long history and strong interest, and its basic rules are simple and easy to understand. A certain school plans to purchase a batch of Chinese chess and Go from Jia Supermarket to enrich students' extracurricular activities. It is known that purchasing $2$ sets of Chinese chess and $3$ sets of Go costs a total of $140$ yuan, and purchasing $4$ sets of Chinese chess and $1$ set of Go costs a total of $130$ yuan.<br/>$(1)$ Find the unit price of each set of Chinese chess and Go;<br/>$(2)$ If the school plans to purchase a total of $80$ sets of Chinese chess and Go, and the total cost does not exceed $2250$ yuan, then how many sets of Go can be purchased at most?<br/>$(3)$ If Jia Supermarket promotes Go: Option 1: Go is all discounted by 10%; Option 2: Apply for a supermarket membership card for $60, and Go is all discounted by 30%. Which option will cost the school less when purchasing Go?

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