
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
Given: The table below shows the situation where type $A$ and type $B$ cars are fully loaded with goods at once:

| $A$ type cars (units) | $B$ type cars (units) | Total goods transported (tons) |
|-----------------------|-----------------------|-------------------------------|
| 3                     | 2                     | 17                            |
| 2                     | 3                     | 18                            |

A logistics company currently has 35 tons of goods and plans to rent $a$ units of type $A$ cars and $b$ units of type $B$ cars simultaneously, with each car fully loaded with goods. Based on the information above, answer the following questions:
  
$(1)$ How many tons of goods can be transported by one unit of type $A$ car and one unit of type $B$ car when fully loaded?
  
$(2)$ Please help design a rental plan for the logistics company.
  
$(3)$ If the rental fee for each type $A$ car is $300$ yuan per trip and for each type $B$ car is $320$ yuan per trip, select the most cost-effective rental plan and calculate the minimum rental cost.

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