
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
In order to enhance students' physical exercise, the school where Xiaoming studies is planning to purchase a certain number of soccer balls and basketballs in bulk from a sports equipment store (with the same price for each soccer ball and each basketball). It is known that purchasing $2$ basketballs and $3$ soccer balls costs a total of $310$ yuan, and purchasing $5$ basketballs and $2$ soccer balls costs a total of $500$ yuan. <br/>$(1)$ How much does each basketball and soccer ball cost? <br/>$(2)$ Based on the actual situation of the school, they need to purchase a total of $60$ basketballs and soccer balls from the store at once, with the total cost not exceeding $4000$ yuan. How many basketballs can they purchase at most?

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