
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
In order to further enrich campus sports activities, a certain middle school is preparing to purchase a certain number of soccer balls and volleyballs at once. The number of soccer balls that can be purchased with $480$ yuan is the same as the number of volleyballs that can be purchased with $390$ yuan. It is known that the unit price of soccer balls is $15$ yuan more than the unit price of volleyballs.  
$(1)$ Find: What are the unit prices of soccer balls and volleyballs, respectively?  
$(2)$ Based on the actual situation of the school, it is required to purchase a total of $100$ soccer balls and volleyballs at once, but the total cost should not exceed $7550$ yuan. How many soccer balls can the school purchase at most?

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