
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 distribution store acts as an agent for a factory to sell a type of building material (here, acting as an agent means that the manufacturer provides the goods for free first, and settlement is done after the goods are sold, with unsold items being handled by the manufacturer). When the selling price is $260$ yuan per ton, the monthly sales volume is $45$ tons. In order to increase operating profit, the distribution store is preparing to promote sales by lowering prices. Market research has shown that when the selling price decreases by $10$ yuan per ton, the monthly sales volume increases by $7.5$ tons. Taking into account various factors, the total cost for selling one ton of building material, including the manufacturer and other expenses, is $100$ yuan.<br/>$(1)$ When the selling price is $240$ yuan per ton, calculate the monthly sales volume at this price;<br/>$(2)$ If the monthly profit of the distribution store is $9000$ yuan, what is the selling price per ton of the material?

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