
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
The school sports group is organizing a badminton club activity and is preparing to purchase two types of rackets, A and B, for students to use. It is known that $1300$ yuan is used to purchase 20 pairs of rackets for each type, with the price of type B rackets being $15$ yuan less than the price of type A rackets.<br/>$(1)$ What are the prices per pair of type A and type B rackets, respectively?<br/>$(2)$ According to the needs, the school decides to purchase a total of 50 pairs of rackets again. Coincidentally, the sports equipment store is having a promotion. The price of type B rackets is reduced by $4$ yuan, and the price of type A rackets is discounted by 20%. If the total cost of purchasing rackets this time does not exceed $1500$ yuan, and the school must purchase at least 38 pairs of type A rackets, what are the possible purchasing plans? Which plan should the school choose to save money? Why?

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