
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: Using $2$ type $A$ cars and $1$ type $B$ car to transport goods at once can carry $10$ tons; using $1$ type $A$ car and $2$ type $B$ cars to transport goods at once can carry $11$ tons.<br/>$(1)$ How many tons can one type $A$ car and one type $B$ car carry at once?<br/>$(2)$ A company has $31$ tons of goods, plans to rent $a$ type $A$ cars and $b$ type $B$ cars at the same time, to transport all goods at once, and each car is fully loaded. What are the possible rental plans for the company?

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