
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 further implement the work of "moral, intellectual, physical, aesthetic, and labor" education, a certain middle school focuses on physical education and plans to purchase a certain number of soccer balls and basketballs at once from a sports equipment store for school ball game activities. The price of each soccer ball is the same, and the price of each basketball is also the same. It is known that the unit price of a basketball is $30 less than twice the unit price of a soccer ball. With the same cost, the ratio of the number of soccer balls purchased to the number of basketballs purchased is $3:2$.
$(1)$ What are the unit prices of soccer balls and basketballs?
$(2)$ According to the actual situation of the school, a total of $200$ soccer balls and basketballs need to be purchased at once, but the total cost of soccer balls and basketballs must not exceed $15500. How many basketballs can the school purchase at most?

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