
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 is preparing to organize $400$ seventh-grade students to participate in a summer camp. It is known that when fully occupied, with $3$ small buses and $1$ large bus, they can transport $105$ students at a time; with $1$ small bus and $2$ large buses, they can transport $110$ students at a time.  
$(1)$ After filling up $1$ small bus and $1$ large bus, how many students can be transported at once?  
$(2)$ If the school plans to rent $a$ small buses and $b$ large buses (they can choose to rent only one type of bus), and transport all students at once, with each bus fully occupied.  
① Please design all possible rental plans.  
② If the rental fee for each small bus is $200$ yuan and for each large bus is $400$ yuan, select the most cost-effective rental plan and calculate the minimum rental fee.

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