
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 has established the following water usage fee standards in order to strengthen citizens' awareness of water conservation. When the monthly water usage per household does not exceed $10$ tons, the water price is $2.2$ yuan per ton. If it exceeds $10$ tons, the excess part is charged at $3$ yuan per ton. A resident in a certain household used $x$ tons of water in the month of July $(x > 10)$, and the water fee to be paid is $y$ yuan. Find:

$(1)$ The relationship between the water fee $y$ and the water usage $x$.

$(2)$ If Xiao Qiang's family paid $67$ yuan for water this month, how many tons of water did they use?

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