
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
China is a country with severe water shortage. In order to enhance the water conservation awareness of its citizens, a certain city has established the following water usage fee standards: when the monthly water usage per household does not exceed 6 tons, the water price is 2 yuan per ton; when it exceeds 6 tons, the excess part is charged at 3 yuan per ton. A resident in this city used x tons of water in May and should pay y yuan for water.  
(1) If 0 < x ≤ 6, write down the functional relationship between y and x.  
(2) If x > 6, write down the functional relationship between y and x.  
(3) If the resident paid 27 yuan for water this month, how many tons of water did the household use this month?

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