
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
Eating zongzi during the Dragon Boat Festival is a traditional custom of the Chinese nation. A supermarket purchased two popular flavors of zongzi, A and B, before the festival. It is known that the amount spent on type A zongzi is $1200, the amount spent on type B zongzi is $800, the quantity of type A zongzi is 50 less than the quantity of type B zongzi, and the unit price of type A zongzi is twice the unit price of type B zongzi.  
$(1)$ Find the unit prices of type A and type B zongzi respectively.  
$(2)$ To meet consumer demand, the supermarket is preparing to purchase a total of 200 type A and type B zongzi. If the total amount does not exceed $1150, how many type A zongzi can be purchased at most?

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