
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
Solving equations and inequalities application problems

Xiao Ming's school is preparing to purchase a certain number of soccer balls and basketballs at once from a sports equipment store to enhance students' physical exercise. The price of each soccer ball is the same, and the price of each basketball is the same. If purchasing 2 basketballs and 3 soccer balls costs a total of $310, and purchasing 5 basketballs and 2 soccer balls costs a total of $500.

(1) How much does each basketball and soccer ball cost?

(2) Based on the actual situation of the school, it is required to purchase a total of 60 basketballs and soccer balls from the store at once, with the total cost not exceeding $4000. How many basketballs can be purchased at most?

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