
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 organized teachers and students to go out for social practice activities and planned to rent buses from a certain car rental company. If they rent $3$ of type A buses and $2$ of type B buses, they can carry $195$ people; if they rent $2$ of type A buses and $4$ of type B buses, they can carry $210$ people.<br/>$(1)$ Please determine how many people each type of bus A and bus B can carry per bus.<br/>$(2)$ If the school has $303$ teachers and students, and the travel agency promises to arrange one tour guide per bus, with the tour guide also needing a seat. Before departure, due to a special situation with one of the tour guides, the travel agency can only arrange for $7$ tour guides. To ensure that each rented bus has a tour guide, the rental plan is adjusted to simultaneously rent three types of buses with capacities of $65$, $45$, and $30$ seats (all three types are rented). At the time of departure, the seats of the three rented buses are exactly full. How should the travel agency arrange the rental plan?

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