
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 middle school organized students for a study tour. The original plan was to rent several $A$ type buses that can seat 45 passengers each, leaving 30 people without seats. If they rent $B$ type buses that can seat 60 passengers each, they can rent 6 fewer buses and fill them exactly.<br/>$(1)$ Find out how many $A$ type buses were originally planned to be rented and how many people went on the study tour this time.<br/>$(2)$ If the school plans to rent a total of 25 buses of types $A$ and $B$, with no more than 7 buses of type $B$, and everyone has a seat, what are the possible rental schemes?<br/>$(3)$ Under the conditions of $(2)$, if the rental fee for type $A$ buses is $220$ yuan per bus and for type $B$ buses is $300 yuan per bus, how should the buses be rented to be most cost-effective?

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