
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
A certain sports equipment store plans to purchase a total of 200 basketballs and volleyballs for sale, with a budget not exceeding $5000. It is known that the cost price of a basketball and a volleyball is $30 and $24 each, respectively. The selling price of each basketball is 1.5 times the selling price of each volleyball. A school purchased basketballs worth $1800 from the store, which is 10 fewer than the number of volleyballs purchased for $1500.<br/>$(1)$ Find the selling price of a basketball and a volleyball each.<br/>$(2)$ In order to benefit consumers, the store decides to reduce the selling price of each basketball by $3 and each volleyball by $2. How should the store purchase the items to maximize profit? (All purchased basketballs and volleyballs are sold out.)

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