
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
The school is preparing to purchase prizes for a "Chinese ancient poetry" recitation competition. It is known that purchasing $3$ type A prizes and $2$ type B prizes from the central market costs a total of $120$ yuan; purchasing $5$ type A prizes and $4$ type B prizes costs a total of $210$ yuan.  
$(1)$ Find the unit prices of type A and type B prizes.  
$(2)$ The school plans to purchase a total of $80$ type A and type B prizes, and the cost of purchasing the prizes this time does not exceed $1500$ yuan. During a promotion at the central market, all items are sold at an 20% discount. Find the maximum number of type A prizes the school can purchase at the central market.

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