
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 freight company currently has 31 tons of goods. They plan to rent $a$ units of type $A$ trucks and $b$ units of type $B$ trucks at the same time to transport all the goods in one go, with each truck being fully loaded. It is known that using 2 type $A$ trucks and 1 type $B$ truck to transport the goods once can carry 10 tons, and using 1 type $A$ truck and 2 type $B$ trucks to transport the goods once can carry 11 tons. Based on the above information, solve the following questions:

1. How many tons of goods can be transported at once by 1 type $A$ truck and 1 type $B$ truck when both are fully loaded?
2. Please help the freight company design a rental plan.
3. If the rental fee for each type $A$ truck is $100 per trip and for each type $B$ truck is $120 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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