
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
【Scenario】During a math activity class, the teacher led the students to the nearby DiDi company to carry out a practical activity on "DiDi billing."  
【Observation】The driver explained that the fare consists of three parts: mileage fee, time fee, and long-distance fee. The mileage fee is calculated based on the actual mileage driven; the time fee is calculated based on the actual driving time; the long-distance fee is charged as follows: within 10 kilometers (including 10 kilometers), no long-distance fee is charged, and for distances exceeding 10 kilometers, an additional fee of $0.4$ yuan per kilometer is charged. The charging standards are as follows:  

| Item       | Mileage Fee     | Time Fee        | Long-Distance Fee |
|------------|-----------------|-----------------|-------------------|
| Unit Price | $1.8$ yuan/km   | $0.45$ yuan/min | $0.4$ yuan/km     |

【Exploration】Based on the above information, answer the following questions:  
The teacher said: If a passenger travels 2 kilometers and the travel time is 4 minutes, then the payment calculation is $1.8 \times 2 + 0.45 \times 4 = 5.4$ yuan.  

【Problem Solving】  
$(1)$ Xiao Dong asked: "According to the teacher's calculation, if my travel distance is 5 kilometers and the travel time is 10 minutes, how much do I need to pay?"  
$(2)$ Xiao Ming asked: "If the travel distance is $a$ kilometers and the travel time is $b$ minutes, how much should I pay?" (Express in algebraic terms containing $a$ and $b$, and simplify).  
$(3)$ The driver said: "If Xiao Wang and Xiao Zhang each take a DiDi Express ride, with travel distances of 9.5 kilometers and 14.5 kilometers respectively, and Xiao Wang's travel time is 24 minutes longer than Xiao Zhang's, the two of them pay the same fare when they get off." Do you agree with the driver's statement? Please explain your reasoning.

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