
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 discount store sells two types of goods, A and B. The cost price of one unit of type A is $40, and the selling price is $60. The cost price of one unit of type B is $50, with a profit margin of 60%.<br/>$(1)$ The profit margin per unit of type A is ______, and the selling price per unit of type B is ______;<br/>$(2)$ If the store purchases a total of 60 units of type A and B, with a total cost of $2600, how many units of each type were purchased?<br/>$(3)$ During the New Year period, the store offers the following promotional discounts for types A and B:<br/><table><tbody><tr><td width="333">Total amount before discount</td><td width="333">Discount</td></tr><tr><td>Not exceeding $380</td><td>No discount</td></tr><tr><td>Exceeding $380 but not exceeding $500</td><td>10% off</td></tr><tr><td>Exceeding $500</td><td>20% off</td></tr></tbody></table>Based on the discount conditions above, if Xiaocong paid $320 for type B on the first day and $432 for type A on the second day, how many units of type A and B did Xiaocong buy in total over these two days?

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