
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 deals with two types of fruits, A and B. The situation of purchasing fruits twice is shown in the table below:

| Purchase Batch | Quantity of Type A Fruit (kg) | Quantity of Type B Fruit (kg) | Total Cost (元) |
|----------------|-------------------------------|-------------------------------|-----------------|
| First          | 60                            | 40                            | 1520            |
| Second         | 30                            | 50                            | 1360            |

Find the purchase prices of type A and type B fruits.

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