
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 taxi fare regulations: the initial price includes a distance of $0$ to $2$ km, and an additional charge is applied for each kilometer beyond $2$ km (less than $1$ km is charged as $1$ km), with an additional $1$ yuan fuel surcharge added to the total fare based on the mileage fee. 

Xiao Zhang said, "I took a taxi from the district government to the train station, a total of $3$ km, and paid a fare of $9$ yuan." 

Xiao Wang said, "I took a taxi from the park to Wanda Plaza, a total of $6$ km, and paid a fare of $15$ yuan." 

$(1)$ What is the initial price of the taxi? How much is the charge for each kilometer beyond $2$ km? 

$(2)$ Xiao Liu took a taxi from a certain square to the airport, walking a total of $18$ km. How much should the fare be?

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