
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 middle school, in response to the call of "bringing football into the campus," purchased two brands of footballs, $A$ and $B$, at a shopping mall. It is known that buying one $B$ brand football costs $30$ yuan more than buying one $A$ brand football. It costs a total of $340$ yuan to buy $2$ $A$ brand footballs and $3$ $B$ brand footballs.<br/>$(1)$ Find out how much it costs to buy one $A$ brand football and one $B$ brand football each?<br/>$(2)$ The school decided to buy a total of $50$ footballs of brands $A$ and $B$. Coincidentally, the prices of the two brands of footballs were adjusted by the mall. The price of brand $A$ footballs increased by $8\%$ compared to the original price, while brand $B$ footballs were sold at a discount of $10\%$ off the original price. If the total cost of buying brand $A$ and brand $B$ footballs this time is $3060$ yuan, then how many brand $B$ footballs did the school purchase?

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