
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 school plans to purchase volleyball and basketball in one go. The price of each basketball is $30$ yuan more expensive than a volleyball. It costs a total of $340$ yuan to buy $2$ volleyballs and $3$ basketballs.<br/>$(1)$ Find the price of each volleyball and basketball.<br/>$(2)$ If the school purchases a total of $60$ volleyballs and basketballs in one go, with a total cost not exceeding $3800$ yuan, and the number of volleyballs purchased is less than $39. Let the number of volleyballs be $m$ and the total cost be $y$ yuan.<br/>① Find the functional relationship of $y$ with respect to $m$ and find all possible values of $m$;<br/>② In what way should the school purchase to minimize the cost? What is the minimum cost?

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