
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
Do not waste the spring days of the four seasons, do not waste the youth of life. In order to experience growth and harvest happiness, the school plans to organize 1000 teachers and students to carry out a study tour activity with the theme of "Joyful Carnival, Challenge to Youth". There are two models of buses, $A$ and $B$, available for rent from a rental company. It is known that one $A$ type bus and one $B$ type bus can carry 75 passengers, and three $A$ type buses and two $B$ type buses can carry 180 passengers.  
$(1)$ Find out how many passengers one $A$ type bus and one $B$ type bus can carry respectively.  
$(2)$ If the rent for one $A$ type bus is 320 yuan and the rent for one $B$ type bus is 400 yuan. The school plans to rent a total of 25 buses of types $A$ and $B$, ensuring that all teachers and students are delivered to the destination and the rental cost does not exceed 9550 yuan. How many rental plans can the school choose?

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