
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 transportation company has two types of trucks, $A$ and $B$. $3$ trucks of type $A$ and $2$ trucks of type $B$ can transport $90$ tons of goods at a time, while $5$ trucks of type $A$ and $4$ trucks of type $B$ can transport $160$ tons of goods at a time.  
$(1)$ Please calculate how many tons of goods can be transported by $1$ truck of type $A$ and $1$ truck of type $B$ at a time.  
$(2)$ Currently, there are $190$ tons of goods that need to be transported. The company plans to arrange trucks of type $A$ and $B$ to transport all the goods at once (with both types of trucks fully loaded). Each truck of type $A$ costs $500$ yuan per trip, and each truck of type $B$ costs $400$ yuan per trip. Please list all possible transportation plans and indicate which plan has the lowest cost.

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