
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
In a seafood market, seafood products need to be transported to various parts of the country. If $5$ type A vehicles and $3$ type B vehicles can transport $370$ tons at a time, and if $4$ type A vehicles and $7$ type B vehicles can transport $480$ tons at a time. <br/>$(1)$ Find out how many tons of seafood products each type A vehicle and each type B vehicle can transport at a time. <br/>$(2)$ In order to ensure the freshness of the seafood and deliver the products to the sales locations in a timely manner, the market manager plans to use $20$ type A and type B vehicles for transportation, with the condition that the transported seafood products are not less than $955$ tons. <br/>① How many type A vehicles are needed at least? <br/>② Given that the cost of transporting with one type A vehicle is $3000$ yuan per trip, and the cost of transporting with one type B vehicle is $2000 yuan per trip, and the total cost is not more than $58800$ yuan, determine which plan requires the least cost and what is the minimum cost?

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