
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 incurs expenses of $600$ yuan per day. The relationship between the number of passengers per day $x$ (people) and the daily profit (profit $=$ ticket revenue minus expenses) $y$ (yuan) is shown in the table below (the fare for each passenger remains constant):

| $x$ (people) | $\ldots $ | $200$ | $250$ | $300$ | $350$ | $400$ | $\ldots $ |
|--------------|-----------|-------|-------|-------|-------|-------|-----------|
| $y$ (yuan)   | $\ldots $ | $-200$| $-100$| $0$   | $100$ | $200$ | $\ldots $ |

Based on the data in the table, answer the following questions:
1. ______ is the independent variable;
2. By observing the data in the table, it can be seen that when the number of passengers reaches ______ or more, the bus will not incur losses;
3. Write down the relationship between the bus's daily profit $y$ (yuan) and the number of passengers per day $x$ (people): $y=$ ______;
4. When the number of passengers in a day is how many people, the profit is $1000$ yuan?

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