
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
The Department of Parks and Gardens in a Forest City is planning to arrange two types of horticultural designs, A and B, with a total of 50 arrangements in the city center. They have 3490 pots of type A flowers and 2950 pots of type B flowers available. It is known that arranging one A type design requires 80 pots of type A flowers and 40 pots of type B flowers, while arranging one B type design requires 50 pots of type A flowers and 90 pots of type B flowers.

1. How many arrangement schemes meet the requirements? Please help design them.
2. If the cost of arranging one A type design is 800 yuan, and the cost of arranging one B type design is 960 yuan, which scheme in (1) has the lowest cost? What is the lowest cost?

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