
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
With the development of economy and technology, the subway, as a green transportation tool, is not only convenient but also environmentally friendly, and is very popular among citizens. A certain city's subway company has decided to implement a segmented discount policy based on the number of passengers passing through the subway station, with the subway fare not exceeding $15$ stations as shown in the table below: $(x \in \mathbb{N}^{*})$

| Number of Stations | $0 < x \leq 4$ | $4 < x \leq 9$ | $9 < x \leq 15$ |
|--------------------|----------------|----------------|-----------------|
| Fare (元)          | $2$            | $4$            | $6$             |

Two passengers, A and B, are both taking the same subway from the starting point, and it is known that they will not exceed $15$ stations on the subway.

$(1)$ If A and B together pay a total fare of $6$ yuan, how many possible scenarios are there for A and B to get off the subway?

$(2)$ If A and B together pay a total fare of $8$ yuan, how many possible scenarios are there for A to get off the subway before B?

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