
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
Taxi driver Li Shifu's operation on the first afternoon of National Day was conducted on a north-south road. If heading south is denoted as "$-$" and heading north is denoted as "$+$", his driving situation that afternoon was as follows: (unit: kilometers, each trip with passengers $)-2,-3,-6,+8,-9,-7,-5,+13.$

$(1)$ When he dropped off the last passenger at the destination, in which direction was he from the starting point in the afternoon? How far was he from the starting point?

$(2)$ If it is stipulated that the starting price for each trip is $10$ yuan, and if the distance traveled in each trip is within $3$ kilometers (including $3$ kilometers), only the starting price is charged. If it exceeds $3$ kilometers, in addition to the starting price, an extra $2$ yuan is charged for each kilometer over $3$ kilometers. How much money did Li Shifu receive from passengers for the taxi fare that afternoon?

$(3)$ If the fuel consumption displayed on Li Shifu's taxi dashboard is $8$ liters per hundred kilometers (the car consumes $8$ liters of fuel per $100$ km), and the price of gasoline is $8$ yuan per liter, without considering the car's wear and tear, did Li Shifu make a profit or a loss that afternoon? How much profit or loss did he make?

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