
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
Mountain bikes are becoming increasingly popular among high school students. A store sells a certain model of mountain bike, with sales of $22,500$ yuan in July of this year. In August, the selling price per bike increased by $100$ yuan compared to July. If the quantity sold in August is the same as the quantity sold in the previous month, the sales amount is $25,000$ yuan.  
$(1)$ Find the selling price per bike in August.  
$(2)$ In order to promote sales, the selling price per bike in September decreased by $15\%$ compared to August. Despite this, the store can still make a profit of $25\%$. Find the cost price of each mountain bike.

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