
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 shop spent $1700$ yuan in May to purchase two types of fruits, A and B. Type A costs $8$ yuan per kilogram, and type B costs $18 yuan per kilogram. In June, the purchase prices of these two types of fruits were increased to $10$ yuan per kilogram for type A and $20$ yuan per kilogram for type B.

1. If the shop purchased the same quantities of these two types of fruits in June as in May, but had to pay an additional $300$ yuan, what were the quantities of type A and type B fruits purchased in May?
2. If in June the shop reduced the total quantity of these two types of fruits to $120$ kilograms, and the quantity of type A did not exceed three times the quantity of type B, what is the minimum amount the shop should pay for these two types of fruits in June?

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