
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
Using $2$ type $A$ cars and $3$ type $B$ cars can transport $18$ tons of goods at once; using $1$ type $A$ car and $2$ type $B$ cars can transport $11$ tons of goods at once. A logistics company currently has $27$ tons of goods, planning to rent both types of cars, $a$ type $A$ cars, and $b$ type $B$ cars, to transport all goods at once, with each car fully loaded.

$(1)$ How many tons of goods can be transported at once by using $1$ type $A$ car and $1$ type $B$ car, each fully loaded?

$(2)$ If the rental cost for each type $A$ car is $100$ yuan per trip, and for each type $B$ car is $120$ yuan per trip. Please help the logistics company design a rental plan and calculate the rental cost.

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