
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
In order to save water, a certain water company adopts the following charging method: if each household uses water not exceeding $15$ tons per month, the charge is $2$ yuan per ton; if each household uses water exceeding $15$ tons per month, the excess part is charged at $2.5$ yuan per ton. In September, Xiao Ming's family used $a$ tons of water.<br/>$(1)$ Express with a formula containing $a$;<br/>When $0\leqslant a\leqslant 15$, the water fee is ______ yuan;<br/>When $a \gt 15$, the water fee is ______ yuan.<br/>$(2)$ When $a=20$, how much money should Xiao Ming pay for water in September?<br/>$(3)$ If Xiao Ming's water bill in September is $55$ yuan, how many tons of water did he use in September?

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