
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
Huhehaote Amber Middle School plans to organize a "Spring Study Tour" activity for teachers and students in the seventh grade. The activity organizer learned the following car rental information from a travel company:

| Car Type | $A$ | $B$ |
|----------|-----|-----|
| Passenger Capacity (people/car) | 50 | 30 |
| Rental Fee (yuan/car) | 400 | 280 |

Based on the actual situation, the school decided to rent a total of 10 cars of types $A$ and $B$, and both types of cars must be rented. The rental cost should not exceed 3500 yuan.

$(1)$ How many cars of type $A$ should the school rent at most?

$(2)$ Under the condition in $(1)$, according to the principle of voluntarism, the school found that a total of 360 people participated in the activity. What are the reasonable car rental options? Which rental method is the most cost-effective?

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