
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
With the enhancement of people's awareness of "energy conservation, environmental protection, and green travel," more and more people prefer to travel by bicycle, which also brings business opportunities to bicycle merchants. The total sales of type $A$ bicycles sold by a certain bicycle shop last year was $80,000. This year, the selling price per unit of this type of bicycle is expected to decrease by $200 compared to last year. If the sales quantity of this type of bicycle remains the same as last year, then this year's total sales will decrease by $10\%$. Find:<br/>$(1)$ How much was the selling price per unit of type $A$ bicycles last year?<br/>$(2)$ The bicycle shop plans to introduce a new batch of $A$ type bicycles and a new type $B$ bicycles totaling $60$ units this year, and the quantity of type $B$ bicycles purchased does not exceed twice the quantity of type $A$ bicycles. It is known that the purchase prices of type $A$ and type $B$ bicycles are $1500$ yuan and $1800$ yuan, respectively, and the planned selling price of type $B$ bicycles is $2400$ yuan. How should the purchases be organized to maximize the profit from the sales of this batch of bicycles?

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