
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
Online car-hailing has become people's preferred way of traveling by car. The billing rules for online car-hailing are as follows:<br/>

| Item     | Starting Fee | Time Fee     | Mileage Fee  | Long-distance Fee |
|----------|--------------|--------------|--------------|-------------------|
| Unit Price | $12$ yuan   | $0.5$ yuan per minute | $2.0$ yuan per kilometer | $1.0$ yuan per kilometer |

Passenger fares consist of four parts: starting fee, time fee, mileage fee, and long-distance fee. The time fee is calculated based on the actual time of the trip; the mileage fee is calculated based on the actual distance traveled; the long-distance fee is charged according to the following standard: within $15$ kilometers (including $15$ kilometers), no long-distance fee is charged. For distances exceeding $15$ kilometers, an additional $1.0$ yuan per kilometer is charged.

$(1)$ Mr. Wang hails an online car for a trip of $20$ kilometers, and the fare he pays is $69.5$ yuan. What is the duration of his trip in minutes?

$(2)$ Xiao Hong and Xiao Lan each hail an online car for trips of $14$ kilometers and $16$ kilometers, respectively. If Xiao Hong's travel time is $1.5$ times that of Xiao Lan's, and both of them pay the same fare, what are their respective travel times in minutes?

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