
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 cultural store plans to purchase two types of instruments, $A$ and $B$, at the same time. If they buy 2 units of type $A$ and 3 units of type $B$, it will cost a total of $1700$ yuan. If they buy 3 units of type $A$ and 1 unit of type $B$, it will cost a total of $1500$ yuan.  
$(1)$ Find the cost price per unit of type $A$ and type $B$ instruments.  
$(2)$ Given that the selling price of type $A$ instrument is $760$ yuan per unit and the selling price of type $B$ instrument is $540$ yuan per unit. The distributor decides to purchase type $A$ and type $B$ instruments without exceeding a total cost of $30000$ yuan. If the number of type $B$ instruments is 3 times that of type $A$ instruments plus 10 units, in order to ensure a total profit of at least $21600$ yuan, what are the possible purchasing plans for the distributor?

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