
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
To conserve water, a city plans to introduce a water pricing policy. The policy states that if a household uses no more than 7 tons of water per month, the price is 3 yuan per ton. If the usage exceeds 7 tons but not 11 tons, the price for the exceeded part is increased by 100%. If the usage exceeds 11 tons but not more than 15 tons, the price for the exceeded part is increased by 200%. Now, suppose a household's actual monthly water usage is $x$ (where $0 \leq x \leq 15$) tons, and the water bill is $y$ yuan.  
(1) Try to find the analytical expression for the function $y=f(x)$.  
(2) If a household paid a total water bill of 126 yuan in the first quarter, with 9 tons used in January and 12 tons in February, find the household's water usage in March.

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