
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 sells apples and pears. It costs 26 yuan to buy 1 kilogram of apples and 3 kilograms of pears, and it costs 22 yuan to buy 2 kilograms of apples and 1 kilogram of pears. <br/> (1) Find the price per kilogram of apples and pears. <br/> (2) If buying a total of 15 kilograms of apples and pears, and the total price does not exceed 100 yuan, then how many kilograms of apples can be purchased at most?

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