
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 supermarket sells two types of mosquito repellent bracelets, type A and type B. One day, they sold 3 type A bracelets and 1 type B bracelet for a total income of $128. Another day, they sold 1 type A bracelet and 2 type B bracelets for a total income of $76.  
$(1)$ What is the price of each type of bracelet?  
$(2)$ A kindergarten wants to buy a total of 100 type A and type B bracelets, with a total cost not exceeding $2500. How many type A bracelets can they buy at most?

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