
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 school wants to establish a drone interest group and needs to purchase two types of drone accessories, type $A$ and type $B$. It is known that purchasing $1$ type $A$ accessory and $3$ type $B$ accessories costs $530$ yuan, and purchasing $3$ type $A$ accessories and $2$ type $B$ accessories costs $890$ yuan.  
$(1)$ Find the cost of purchasing $1$ type $A$ accessory and $1$ type $B$ accessory each.  
$(2)$ The school decides to purchase a total of $30$ type $A$ and type $B$ accessories, with a total cost not exceeding $4180$ yuan. How many type $A$ accessories can be purchased at most?

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