
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 certain number of soccer balls and basketballs at once from a sports equipment store to enrich the students' campus life. The price of each soccer ball is the same, and the price of each basketball is the same. If purchasing $4$ soccer balls and $7$ basketballs costs a total of $740$ yuan, and purchasing $7$ soccer balls and $5$ basketballs costs a total of $860$ yuan. <br/>$(1)$ How much does it cost to purchase one soccer ball and one basketball each? <br/>$(2)$ Based on the actual situation of the school, it needs to purchase a total of $50$ soccer balls and basketballs at once from the sports equipment store, with the total cost not exceeding $3600$ yuan. How many soccer balls can the school purchase at most?

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