
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
Experimental Middle School plans to enrich students' campus life by making a one-time purchase of several footballs and basketballs (the price of each football is the same, and the price of each basketball is the same). If they buy 3 footballs and 2 basketballs, the total cost is 310 yuan. Buying 2 footballs and 5 basketballs costs 500 yuan.  
(1) How much does it cost to buy one football and one basketball?  
(2) Experimental Middle School actually needs to buy a total of 96 footballs and basketballs at one time. The total cost of buying footballs and basketballs must not exceed 5800 yuan. What is the maximum number of basketballs the school can buy?

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