
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 plans to organize all eighth-grade teachers and students to conduct a study tour at a red base. They need to rent a total of 6 buses of type A and type B. It is known that the rental fees for type A and type B buses are $450 per bus and $300 per bus, respectively. Let $x$ represent the number of type B buses rented, and the rental fee be $y$ yuan.  
$(1)$ Find the expression of $y$ in terms of $x$ (state the range of the independent variable $x$);  
$(2)$ If the number of type B buses rented is less than the number of type A buses rented, how many type B buses should be rented to minimize the rental fee? What is the minimum cost?

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