
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
The Foshan Education Bureau recently issued a notice on the organization of the city's junior high school graduation sports exam in 2023, which determined that students can choose the exam items by themselves. A certain school plans to purchase a batch of basketballs and soccer balls to ensure that the ninth-grade graduates have enough training equipment. If they buy 20 soccer balls and 15 basketballs, the total cost is 2050 yuan; if they buy 10 soccer balls and 20 basketballs, the total cost is 1900 yuan.  
$(1)$ What is the price of each soccer ball and basketball?  
$(2)$ If the school plans to use no more than 2800 yuan to purchase a total of 50 soccer balls and basketballs, with the number of soccer balls not exceeding three times the number of basketballs, how many basketballs can they buy at most?

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