
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 bus has a monthly expenditure of $4000. The relationship between the number of passengers per month $x$ (people) and the monthly profit ($y$ in dollars) is shown in the table below (the bus fare for each passenger remains constant).

|x (people)|500|1000|1500|2000|2500|3000|...|
|---|---|---|---|---|---|---|---|
|y (dollars)|-3000|-2000|-1000|0|1000|2000|...|

$(1)$ In this changing process, the independent variable is ______; the dependent variable is ______;  
$(2)$ By observing the data in the table, it can be seen that the bus will not incur losses unless the monthly passenger volume reaches at least ______ people;  
$(3)$ Predict the monthly profit when the number of passengers per month is 4230 people?

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