
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
There are two types of trucks, large and small. $3$ large trucks and $4$ small trucks can transport $18$ tons of goods at once, while $2$ large trucks and $6$ small trucks can transport $17$ tons of goods at once. <br/>$(1)$ How many tons of goods can $1$ large truck and $1$ small truck transport respectively at once? <br/>$(2)$ Currently, there are $33$ tons of goods that need to be transported. The transportation company plans to arrange a total of $10$ trucks, including both large and small trucks, to transport all the goods at once. It costs $130$ yuan for each large truck to transport goods at once, and $100$ yuan for each small truck. How should the transportation company arrange the trucks to minimize costs? What is the minimum cost?

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