
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 school is preparing to purchase a batch of soccer balls and basketballs. From a sports store, they learned that one soccer ball and three basketballs cost $275$ yuan, and three soccer balls and two basketballs cost $300$ yuan.  
$(1)$ Find the price of one soccer ball and one basketball.  
$(2)$ If the school plans to purchase a total of $80$ soccer balls and basketballs, and the number of soccer balls is not more than three times the number of basketballs, design the most cost-effective purchasing plan and explain the reasoning.

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