
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 fruit store purchased two newly produced fruits, A and B, for a total of 140 kilograms with $1000. The purchase price and selling price of these two fruits are shown in the table below:

|         | Purchase Price (元/kg) | Selling Price (元/kg) |
|---------|------------------------|-----------------------|
| Fruit A | $5                     | $8                    |
| Fruit B | $9                     | $13                   |

$(1)$ How many kilograms of each fruit were purchased?

$(2)$ If the fruit store sells this batch of fruits at the selling price, how much profit will they make?

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