
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
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?

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