
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
Residents in a certain city are charged for using tap water according to the following standards: if the water usage per household does not exceed $12m^{3}$, they are charged at a rate of $a$ yuan/$m^{3}$; if it exceeds $12m^{3}$ but does not exceed $20m^{3}$, the excess part is charged at $1.5a$ yuan/$m^{3}$; if it exceeds $20m^{3}$, the excess part is charged at $2a$ yuan/$m^{3}$.

$(1)$ Fill in the blanks as required: 
① When a user uses $18m^{3}$ of water, the amount charged is ______ yuan; 
② When a user uses $26m^{3}$ of water, the amount charged is ______ yuan; 
③ When a user uses $n$ amount of water $(n > 20)$, the amount charged is ______ yuan.

$(2)$ If $a=1.5$, then when the water bill for a user last month was $60, write down the value of $n$ directly.

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