
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 the following water usage fee standards: for each household, if the monthly water usage does not exceed $6m^{3}$, the water fee is charged at a rate of $a$ yuan per cubic meter; if it exceeds $6m^{3}$, the part that does not exceed is still charged at $a$ yuan per cubic meter, and the part that exceeds is charged at $b$ yuan per cubic meter. The water usage situation of a household in the city this year is as follows:

| Month | Water Usage $(m^{3})$ | Water Fee (yuan) |
|-------|-----------------------|------------------|
| 3     | 5                     | 7.5              |
| 4     | 9                     | 27               |

$(1)$ Find the water fee when the user's water usage is $x m^{3} (x > 6)$ (expressed as an algebraic expression with $x$).  
$(2)$ A user paid a water fee of 39 yuan in a certain month. How many cubic meters of water did the user use that month?

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