
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
Football is the world's number one sport. The 2022 World Cup once again ignited people's passion for football. During the World Cup, a stationery store in Guangming District purchased two types of footballs, A and B, for a total of 200 balls at a cost of 14400 yuan. The purchase price and the marked price of the two types of footballs are shown in the table below:

| Category | Football A | Football B |
|----------|------------|------------|
| Purchase Price (yuan per ball) | 80 | 60 |
| Marked Price (yuan per ball) | 120 | 90 |

$(1)$ Find out how many balls of type A and type B were purchased by the stationery store.  
$(2)$ In order to accelerate sales and recover funds, the stationery store decided to sell football A at an 20% discount and football B at a 10% discount. If all the purchased footballs are sold, how much profit will the stationery store make?

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