
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
During the Double 11 shopping festival, a certain online store purchased two types of toys, $A$ and $B$, directly from the factory. The purchase price and selling price are as shown in the table: (Note: Profit = Selling Price - Purchase Price)

|          | $A$ toy | $B$ toy |
|----------|---------|---------|
| Purchase Price (元 per item) | $28$ | $24$ |
| Selling Price (元 per item) | $40$ | $36$ |

$(1)$ If the online store purchases a total of $50$ toys of types $A$ and $B$ for $1320$ yuan, find the number of each type of toy purchased.  
$(2)$ After the Double 11 festival, the online store plans to reduce the price of type $A$ toys for sale. If sold at the original price, an average of $8$ toys can be sold per day. For each yuan reduction in price, an average of $1$ additional toy can be sold per day. What should be the selling price per item of type $A$ toys in order to make the average daily profit from selling type $A$ toys $96$ yuan?

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