
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 school plans to rent two types of buses, A and B, to transport 180 teachers and students to a research base for comprehensive practical activities. It is known that renting one bus of type A and one bus of type B costs a total of $500, and renting 2 buses of type A and 3 buses of type B costs $1300. Each bus of type A can accommodate 15 teachers and students, and each bus of type B can accommodate 25 teachers and students.  
$(1)$ How much does it cost to rent each bus of type A and type B?  
$(2)$ If the school plans to rent 8 buses, how should they rent the buses to minimize the total cost?

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