
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
To enrich students' campus life, a certain school is preparing to carry out colorful club activities. The school purchases supplies in a timely manner based on the number of students enrolled in courses to ensure the smooth running of club activities. It is known that $6$ sets of chess and $5$ sets of Go cost a total of $190$ yuan, and $8$ sets of chess and $10$ sets of Go cost a total of $320$ yuan. <br/>$(1)$ Find the unit price of chess and Go; <br/>$(2)$ Considering the expansion of enrollment in the second year, the school plans to purchase chess and Go again with a budget of no more than $1800$ yuan, totaling $100$ sets. If the unit price remains the same, how many sets of chess can be purchased at least?

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