
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 city is holding a knowledge competition on "Creating a National Civilized City". It is known that buying one type A prize and 2 type B prizes costs $220$ yuan, and buying 2 type A prizes and 3 type B prizes costs $360$ yuan.<br/>$(1)$ Find the price of each type A prize and each type B prize, respectively?<br/>$(2)$ If it is planned to buy a total of 30 type A and type B prizes, with a total cost not exceeding $2300$ yuan, then how many type A prizes can be purchased at least?

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