
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 response to the national call for "football into schools," a certain school purchased $50$ type $A$ footballs and $25$ type $B$ footballs for a total of $7500$ yuan. It is known that buying one type $B$ football costs $30$ yuan more than buying one type $A$ football.<br/>$(1)$ Find out how much it costs to buy one type $A$ football and one type $B$ football each?<br/>$(2)$ Through the joint efforts of the teachers and students of the whole school, the school has been awarded the title of "Football Featured School" this year. The school plans to purchase $50$ footballs of type $A$ and type $B$ again with a budget of no more than $4800$ yuan. If the unit price remains the same, how many type $A$ footballs can be purchased at least this time?

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