You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
In 2016, the price of a certain small commodity was 15 yuan/piece, and the sales volume was $a$ pieces. The distributor plans to reduce the price of this commodity to between 10 yuan/piece and 14 yuan/piece in 2017. After investigation, the expected price by customers is 7 yuan/piece. According to market research, the increase in sales volume after the price reduction is inversely proportional to the difference between the set price and the customer's expected price, with a proportionality constant $k$. The cost price of the commodity is 5 yuan/piece.  
(1) Write the function relationship between the distributor's annual income $y$ and the set price $x$ after the price reduction;  
(2) Let $k=3a$. When the set price is how much, the distributor's income in 2017 is exactly 1.2 times the income of 2016?
user
x=13
rule
In 2016, the price of a certain small commodity was 15 yuan/piece, and the sales volume was $a$ pieces. The distributor plans to reduce the price of this commodity to between 10 yuan/piece and 14 yuan/piece in 2017. After investigation, the expected price by customers is 7 yuan/piece. According to market research, the increase in sales volume after the price reduction is inversely proportional to the difference between the set price and the customer's expected price, with a proportionality constant $k$. The cost price of the commodity is 5 yuan/piece.  
(1) Write the function relationship between the distributor's annual income $y$ and the set price $x$ after the price reduction;  
(2) Let $k=3a$. When the set price is how much, the distributor's income in 2017 is exactly 1.2 times the income of 2016?
train