
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
The relationship between the taxi fare (in yuan) during the day and the mileage $x$ kilometers in a certain city is as shown in the table below. $9$ is the starting price, and for distances less than $1$ kilometer, a charge of $1$ kilometer is applied:

| Mileage $x$ kilometers | $0\leqslant x\leqslant 3$ | $4$ | $5$ | $6$ | $7$ | $\ldots $ |
|------------------------|--------------------------|----|----|----|----|----------|
| Fare (yuan)            | $9$                      | $1.2+9$ | $2.4+9$ | $3.6+9$ | $4.8+9$ | $\ldots $ |

$(1)$ Express the algebraic expression of the taxi fare for mileage $x (x>3)$;  
$(2)$ The distance from the city's train station to a certain scenic area is approximately $19.4$ kilometers. How much money should be prepared to take a taxi?  
$(3)$ If Xiaohuang pays $19.8$ yuan for the taxi ride, approximately how many kilometers did the taxi travel?

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