
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 a traditional school for table tennis sports. In order to further promote the development of this sport, the school is planning to purchase several pairs of straight paddles and horizontal paddles from a sports equipment store. For every pair of paddles purchased, they must also buy 10 table tennis balls. The price of each table tennis ball is $2$ yuan per ball. If they spend $9000$ yuan on purchasing 20 pairs of straight paddles and 15 pairs of horizontal paddles, and spend $1600$ yuan more on purchasing 10 pairs of horizontal paddles compared to purchasing 5 pairs of straight paddles.<br/>$(1)$ Find the price of each type of paddle per pair.<br/>$(2)$ If the school purchases a total of 40 pairs of paddles, and the number of straight paddles purchased is not more than three times the number of horizontal paddles purchased, provide a cost-effective solution and calculate the total cost for this solution.

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