
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 supermarket plans to purchase a batch of two types of goods, A and B, at the same time. If they buy 10 items of type A and 8 items of type B, it will cost $880$ yuan. If they buy 2 items of type A and 5 items of type B, it will cost $380$ yuan.<br/>$(1)$ Find the cost price per item of goods A and B, respectively.<br/>$(2)$ The supermarket plans to purchase a total of $50$ items of these two goods, with a budget not exceeding $2520$ yuan. According to the market price, the selling price of goods A is $50$ yuan, and the selling price of goods B is $75$ yuan. The supermarket hopes to make a profit of at least $620$ yuan after selling all these goods. How many purchasing plans does the supermarket have?

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