
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 "Kiwi" business owner has two types of "Kiwi" for promotion, type \\(A\\) and type \\(B\\). If you buy 2 pieces of type \\(A\\) "Kiwi" and 1 piece of type \\(B\\) "Kiwi", the total cost is 120 yuan; if you buy 3 pieces of type \\(A\\) "Kiwi" and 2 pieces of type \\(B\\) "Kiwi", the total cost is 205 yuan.

\\((1)\\) Let the price per piece of type \\(A\\) and type \\(B\\) "Kiwi" be \\(a\\) yuan and \\(b\\) yuan, respectively. Find the values of \\(a\\) and \\(b\\).

\\((2)\\) The cost price of each piece of type \\(B\\) "Kiwi" is 40 yuan. According to market research: if sold at the unit price found in \\((1)\\), the "Kiwi" business owner sells 100 pieces of type \\(B\\) "Kiwi" per day; if the selling price increases by 1 yuan, the daily sales volume of type \\(B\\) "Kiwi" decreases by 5 pieces. Find the selling price per piece that maximizes the daily profit of type \\(B\\) "Kiwi", and what is the maximum profit?

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