
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, was called "Yi" in ancient times, is the ancestor of board games. Go has a history of more than 4000 years. Chinese chess is also a cultural treasure of the Chinese nation, with a long history and strong interest. The basic rules are simple and easy to understand. A school wants to liven up students' extracurricular activities by purchasing a batch of Chinese chess and Go. It is known that buying 2 sets of Chinese chess and 1 set of Go costs a total of $80, and buying 4 sets of Chinese chess and 3 sets of Go costs a total of $190. <br/> $(1)$ Find the unit price of each set of Chinese chess and Go; <br/> $(2)$ The school plans to purchase a total of 120 sets of Chinese chess and Go, with a total cost not exceeding $3500. How many sets of Go can be purchased at most?

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