
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 city implements a tiered water fee system for residents. If the monthly water consumption of a household does not exceed $20t$, the fee is $1.9$ yuan per ton. If the monthly water consumption exceeds $20t$, the part that does not exceed $20t$ is still charged at $1.9$ yuan per ton, and the excess part is charged at $2.8 yuan per ton. Let the monthly water consumption of a household be $x$ tons.  
$(1)$ Write down how much water fee should be charged when the monthly water consumption of a household does not exceed $20t$ and exceeds $20t$, respectively.  
$(2)$ If the average water fee for a resident in this city in May is $2.3$ yuan per ton, how many tons of water did the resident use in May?

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