
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 very popular among high school students. A model of mountain bike sold by an online store had sales of $27,000 in January this year. In February, the selling price per bike decreased by $100 compared to January. If the quantity sold in February is the same as the quantity sold in January, the sales amount is $24,000.  
$(1)$ Find the selling price per bike in February.  
$(2)$ In order to promote sales, the selling price per bike in March decreased by $10% compared to February. The online store still made a profit of $44\%$. Find the cost price of each mountain bike.

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