
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 uses price control measures to achieve water conservation. The price list for the city's tap water charges is as follows: (Water fees are settled monthly, where $m^{3}$ represents cubic meters)

| Monthly Water Usage | Price |
|---------------------|-------|
| Not exceeding $8m^{3}$ | $2$ yuan/$m^{3}$ |
| Exceeding $8m^{3}$ but not exceeding $12m^{3}$ | $3$ yuan/$m^{3}$ |
| Exceeding $12m^{3}$ | $5$ yuan/$m^{3}$ |

Based on the content of the price list, answer the following questions:
$(1)$ If Xiao Cong's household uses $10m^{3}$ of water in May, the water fee should be ______ yuan. (Write down the answer directly)
$(2)$ If Xiao Ming's household uses $am^{3}$ of water in June (where $a \gt 12$), find out how much Xiao Ming's household should pay for water in June? (Express the answer in terms of $a$, show the process, and simplify)

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